Quite a good question. I'd like to tackle it in pieces;
Yes. Regardless of the name used, they all derive from a martial art based theory.
Ideally, no. Realistically, yes.
Martial art is an all encompassing term theses days. Originally, a martial art was meant, in large part, for one thing....defeating an attacker in armed or unarmed personal combat. Yes, esoteric venues have been attached to it through the years such as sport, health, social interaction etc. But martial arts in-and-of-themselves are movements designed to cause injury and/or pain to another for self-preservation or to defeat an action. Nowadays however, martial arts may mean self-defense or it may mean twirling a glow in the dark 'numchuck' to music in order to compete for a trophy or ribbon. It may mean its the thing you do Mondays and Thursdays while Tuesdays and Fridays are reserved for bowling. Or it could mean, for some folks, a means of training to protect yourself in armed or unarmed combat. Ask 10 different 'martial artists' and you'll likely get 10 different answers.
Defensive Tactics (D.T.) is usually the term used in law enforcement. It is the term I/we use when we're teaching L.E. and Corrections academies. While used for self-protection, D.T. also covers techniques that can be used to transport or secure an individual. Terms such as 'bent wrist' or 'goose neck' are used as well as 'hammer lock' and 'pain compliance'. It is usually a VERY simple course. The techniques have sound principles that IF trained for consistently will often produce positive results. Unfortunately, the bulk of L.E. and Corrections doesn't routinely train with D.T. or firearms beyond the academy. The individual that goes on to take martial arts or advance D.T. (or shooting for that matter) are few and far between. Such advanced D.T. course include such programs as S.P.E.A.R. (SPontaneous Enabling Accelerated Response) by Tony Blauer, PCR (Physical Conflict Resolution) by Gen Good (Seal Team Six), Boatman's Edged Weapon Defense by the late Sir Peter Boatman or Israeli Instinctive Shooting and/or Israeli Urban Survival (Hisardut Krav Maga) by several former Israeli commandoes. I've taken the instructor course for each of these and they are, hands down, among the most hard-core D.T. combatives courses out there. I'd place them in the H2H section as well.
Self-Defense can be contained within the martial arts or D.T. sections. It could also be a short-term course designed for the civilian that doesn't take further education in the venue. Just as with D.T., it usually offers simple but effective methods of (usually) unarmed defense. If the person would train with such methods, at least periodically they would likely be well served for the majority of altercations they may find themselves in. If they don't....well we train to live and live to train is the old saying.
H2H is basically (usually) meant for military (or advanced L.E./Corrections team/individuals). More than self-defense, it could be termed self-offense just as easily. H2H often is doing something dynamic and terminal to someone as opposed to defensive movements designed to defeat an attacker. Fathers of modern H2H would include William Fairbairn, Pat 'Dermott' O'Neill, Col. Rex Applegate, Charles Nelson, Carl Cestari and others. Without trying to make a shameless plug for Martial Warrior, there are a collection of articles and videos in the SD section for anyone interested http://excoboard.com/martialwarrior/148250. H2H reading material would include 'Kill or be Killed' and 'Get Tough'. As an interesting note, and I've mentioned this before, Pat 'Dermott' O'Neill of WW2 combatives fame was at one time the highest ranked non-Japanese Judoka in the world. His WW2 H2H combatives teaching included NO Judo of any kind. No sporting elements went into its development. He was quite strict on that point.
H2H was trained quickly and trained hard. Often less than 24 hours of training. Yet it was all based on gross motor skill by rote to be retained in long term memory and highly usable under duress. It succeeded. There are cases such as the senior citizen (and former FSSF member) who took out an armed robber at a 7-11 based ONLY on what he learned from O'Neill back in WW2. As I said, retained in long term memory was the goal of the training. My step-father told me of a similar incident involving the town drunk who at one time was also a WW2 combatives trainer. Suffice it to say that no one picked on him after an incident.
Hope this may have been of some interest. If the OP doesn't mind, I'm going to put this on MW as well as it is really a good question and I don't want to have to retype my post.
Stay safe everyone
Good points! By all means please feel free to put it on your MW!