Hmm. Okay.
How would someone know you were training in Toshindo? They probably wouldn't. They may pick up that you have trained in a Ninjutsu-related system (Bujinkan, Genbukan, Jinenkan, Toshindo etc), but that would probably be about it. In this regard, it's similar to knowing that the person you're watching is trained in Wado Ryu Karate, or Goju Ryu Karate. If you're very well versed, then you may pick up on the differences, but overall, you would probably be able to pick up "Karate", and that's all.
In terms of the technical characteristics of Ninjutsu-related systems, as mentioned earlier, they are Japanese arts, so they will have a higher focus on grappling over striking (the Koto Ryu is rather unusual in Japanese systems with the amount of striking they use). But the big thing to remember here is that Toshindo, like all the other major organisations, blends the skills and techniques of a number of old systems, the Togakure Ryu, Gyokko Ryu, Koto Ryu, Hontai Takagi Yoshin Ryu, Shinden Fudo Ryu, and Kukishinden Ryu, and each of these arts have their own "flavour" or characteristics. For example....
Togakure Ryu Ninpo Taijutsu has no strike or kick defence in it's scroll, which is made up exclusively of weapon and grab defences and escapes, incoporating a range of close quarter weaponry, as well as having a dedicated sword scroll. It's most characteristic posture (kamae) is known as Doko no Kamae, or Mad Tiger, and is defensive and evasive in nature. All techniques have a definate strategy to them, which is to stay out of range, then suddenly move inside the opponents space, perform your technique, then escape and get distance again. I refer to this art as "the art of escape", or, when I'm in a more fun mood, "the art of running away!" This, more than any other system within the syllaus, shows the guerilla "hit-and-run" tactics said to be so typical of the ninja.
Gyokko Ryu is one of the oldest systems around, and it's history of utilising armour (coming from a time of very heavy O Yoroi) gives it a 50/50 weight distribution for most of it's postures. The most characteristic posture is Ichimonji no Kamae (Number One Posture), again a defensive posture similar to Doko (for what it's worth, Gyokko also has a posture they refer to as Doko no Kamae, which is similar, but different to the Togakure Ryu one). The other primary posture is Jumonji no Kamae (Number Ten Posture), a guarded offensive posture. The primary tactic of Gyokko Ryu is to constantly change direction on the attacker, by leading them first in one direction (say, left), then suddenly switching to move them to the right. This increases the effect of limb controls and joint locks to a quite devestating level. It also focuses on use of fingers and the tip of the thumb to a great effect. I refer to this system as "the art of changing direction", for obvious reasons.
Gyokko gives most of the basics to the various Ninjutsu organisations, in the form of the Sanshin no Kata, and the Kihon Happo. It is also one of only two well known martial arts said to have been founded by a woman (possibly a princess or lady-in -waiting in China. The skills were brought to Japan later). There are a set of rules associated with this school.
Koto Ryu, as I said, features more striking than is typical in Japanese systems. This is said to be a hallmark of it's history travelling from China, to Korea, and then to Japan. One theory as to the origin of Koto Ryu in Japan is that the then-current Soke of Gyokko Ryu, SakagamiTaro Kunishige, was finding that Gyokko Ryu was not being successful on the battlefield. He came into contact with the knowledge brought from China via Korea, and adapted both his system (which he reorganised from Gyokko Ryu Shitojutsu as it was known to Gyokko Ryu Kosshijutsu, which it remains to today), and structured the new knowledge to form Koto Ryu.
The primary postures include Seigan no Kamae, a defensive posture, Bobi no Kamae, and offensive one, and Hoko no Kamae, a recieving posture. It is characterised by a great deal of forward movement (very little backwards movement, most evasions are sideways instead), and quite a lot of offensive, or attacking techniques. It is said that the Gyokko Ryu used to practice their techinques against the attacking rhythms of Koto Ryu, as these two arts have been taught together since Koto Ryu was founded. I refer to this systems as "the art of striking", or more simply, "just hit them!".
Takagi Yoshin Ryu is a very typical traditional Japanese Jujutsu system. The focus is on joint locks, throws, and chokes, and is a very compilcated, involved system, with a range of strategies and tactics, and very few formal postures (most schools simply use ones known from other systems), although it does have it's own form of Seigan, and unique ways of sitting in Seiza and Fudoza. Most of the Muto Dori, or unarmed techniques against swords (and other weapons) are from this school. It also has a reputation as "the bodyguard school" as in previous generations it was learnt by a family that acted as bodyguards for a powerful Daimyo. My personal feeling of this school, even though it covers such a great range, is simple. This I refer to as "the art of no hesitation".
Shinden Fudo Ryu actually has two components to it (some believe that they are actually different schools... I have heard both. Manaka Sensei when he was with the Bujinkan taught that they were different aspects of the same school, others have classed them as different with different lineages). I'll treat them here seperately.
Shinden Fudo Ryu Dakentaijutsu is a suhada (unarmoured) jujutsu system, again liek Takagi Yoshin Ryu taking a variety of tactics to get it's teachings across. It's a rather direct school, and I like to think of it like Koto Ryu but focused on grappling rather than striking. Along with the Takagi Ryu, this is where the seated techniques come from (suwari waza), including some quite odd muto dori techniques. This system has no postures whatsoever, and has a highly emphasised focus on being natural in all ways. Early teachings said that you should learn in nature, using what is found around before creating a dojo (building) and using training tools. For this reason (and it's technical approach matching this ideal) I refer to this as "the art of nature".
Shinden Fudo Ryu Jutaijutsu (Taijutsu) is rarely taught in the Bujinkan, and I don't know if it is featured in the Toshindo curriculum. It is taught in the Jinenkan and the Genbukan, though. It is a much rougher jujutsu form, with very nasty throws (a quite vicious habit of applying a forward hip-throw while applying a musha dori/gyoja dori... honestly, that is just vicious). This system has 5 postures associated, focused around it's version of Seigan.
Kukishinden Ryu is a battlefield system originally focused on the Naginata and spear, and later the focus changed to staff weapons, the bo in particular. The unarmed part is designed to work in armour, or without, and has a high emphasis on chaining joint locks and applying high impact throws. I tend to say that Kukishinden Ryu Dakentaijutsu is designed to take someone and turn them upside down (so they end up on their head) as quickly as possible. Again, a range of postures, most typical being Kosei no Kamae, a guarded offensive posture. This is also where most of the weapon skills come from. I refer to this school as "the art of the battlefield" for again obvious reasons.
Did that help? I expect not. That's what I meant when I said the only way to really know what makes it this particular art is to train it.
But, to tide you over, look to things like a slight weight shift to the rear, lead hand extended, and rear guarding your chest, with the hand typically on the bicep (Seigan, Ichimonji, and various others), a shuto ken (hand edge strike) will be done with a cupped hand, rather than the straight edge that karate tends towards, there is a frequent use of anges, not just forward and backward, or to the sides, kicks are typically low (the most common target in the scrolls is the ribs or groin crease, followed by the groin, then lower to the knees) and straight, with the impact (for a foot stomp) with the heel, by turning the foot out, a common attack in traditional patterns is a stepping lead punch, most of the time the same hand and foot are always forward (Koto is the biggest excpetion to this, with Togakure a close second), a large emphasis on rolling and weaponry, probably the most common posture of all is Shizen no Kamae, which actually doesn't come from any of the schools (although a few have similar concepts with different names, most commonly Hira no Kamae, sometimes Shizentai), which is a natural posture, essentially just standing there with no preparation. Toshindo then also has a high focus on modern self defence, taking these traditional concepts and strategies and tactics, and applying them against modern street-style attacks.
Okay, I think that should do it. Hope this has helped.