Well, this seems to come up a every now and then, so I'm just going to put down a few answers to these and other questions that have come up more than once. Let's have some fun, shall we?
First off, let's look at the terms themselves.
Katana is written with this character - 刀 -, and it basically just means "blade", and often is used to represent "sword". It is alternately pronounced "To", which is the on'yomi ("sound" pronunciation) of the character (in other words, the way the old Japanese thought the Chinese pronounced the same character, from whom they took the written symbols). For the record, the Chinese pronunciation is "Dao", and refers to "blade", often translated as "knife, or sword". This character is then found in other weapons such as Tanto (短刀 - a knife, literally a short blade), Shoto (小刀 - short sword, literally small blade), or Daito (大刀 - long sword, literally big blade). As a result, a katana really only refers to a bladed weapon or sword, almost regardless of characteristics (at least, on paper....).
Tachi, on the other hand, is written with the characters - 太刀 - , and it literally translates as "thick blade, or sword" (slightly different to Daito, you may notice).
There is then another term which specifically refers to a sword, which is pronounced as Tsurugi, or Ken (which is the on'yomi pronunciation... the Chinese pronunciation is "Jian"), and is written with the character - 剣. This term originally referred specifically to an early straight sword, with two edges, basically copied along with the rest of the Court culture from China to mark the Heian Period (Peaceful Period) of the 10th - 12th Century, but was further applied to the curved blades that began to be seen in the mid-late Heian, most famously blades such as the Kogarasu Maru, attributed to Amakuni.
(Small rant here: The above is written in part in answer to a video of Kacem Zhougari where he claims that To/Katana only refers to curved blades, and Ken/Tsurugi only refers to the older straight blades, and therefore "Kenjutsu" and "Kendo" are inaccurate terms, whereas "Tojutsu" is correct. This is to give credence to his Gyokko Ryu Tojutsu etc that he teaches... I am rather unconvinced of the validity of this teaching, or the validity of his linguistic argument. Okay, rant over.
PS Video here:
Right, rant done now. Promise.)
Right, to the differences. Er... not much, really. As covered, the main way to differentiate a tachi from a katana is the way it is mounted and worn (with the location of the mei, or signature, being the only way to determine whether a particular blade was originally intended to be worn/mounted as a katana or tachi,
if it is present!). Some tachi were seen to have a deeper sori, or curvature, but that realistically wasn't actually the case. What they actually had was a differently placed sori, having the greater portion of the curve being nearer the tsuba in a form known as koshi sori (as opposed to nearer the tip, saki sori, or evenly in the middle, torii sori... there was a rare one as well, mainly found in tanto, where the very end of the weapon curved back towards the front, rather than back, known as uchi sori). This koshi sori allowed the tachi to be more easily drawn on horseback (which was also the reason for it's mounting form.... incidentally, a tachi could be mounted and worn edge up in the obi [belt] when it was worn by a gunner, mainly to keep it from dragging or knocking on the ground when they knelt to fire their guns). The blade itself may also not be much longer than a "typical" katana, particularly if it's an early example, as the shorter, lighter weapons were much easier to handle one-handed on horseback once you got too close for the bows and arrows that were actually the samurai's stock in trade and most identifiable weapon.
The longer tachi appeared later in Japan's history, when mounted archery stopped being the dominant form of warfare in Japan, and in close fighting was more common. The curve at this time moved more to the typical katana-style torii sori, while the weapons became more oversized to handle the long reach advantage of the pole-arms such as naginata or yari. It may also be noted that at this time the katana began to be developed, initially being the secondary side-arm to the tachi, and referred to as an uchigatana (striking sword, implying that it was used to strike the final blow in in-fighting), and was worn edge up in the belt. When it became the primary weapon of the samurai (during peacetime, it may be noted), and moved to take the place of the tachi, the wakizashi (literally: inserted at the side, meaning that it was put into the obi on the side of the katana) was developed to take the place of the katana.
In terms of size of weaponry, during the Edo period, the Tokugawa Shogunate issued a range of edicts to control the warriors under them, and amongst them were edicts governing the length of swords, which limited them to less than two and a quarter feet in length. Before that, it was really up to the individual warrior themselves, and the Ryu to which they belonged. For example, the Kage Ryu maintained their favour for oversize weapons, despite the edict. In fact, in stark defiance, they have a
minimum length which is nearly half a foot longer than the Tokugawa prescribed length. Other schools such as Shinmuso Hayashizaki Ryu use very long weapons, despite the edicts. All of these weapons are referred to as "katana" in the Ryu that use them. Tachi, on the other hand, were commonly found in the early periods (Heian, Kamakura etc) at even less than two feet blade length. So length is really no indicator at all.
Confused yet?