In most games, a normal move (or just a ‘normal’) is a move you can use by pressing a single button. They correspond to the system of buttons for a particular game.
Normal moves can be divided into various categories, which differ mostly on statuses and divisions (further explained further down).
Depending on what they are, normal moves can be useful in combos, anti-air, jump checking, zoning, and so on, so there are plenty of cases where normal moves can be said to be more critical than special moves.
Players just past beginning level (and some plain old not-so-good players) have a tendency to put too much stress on the abilities of special moves. But... no normals, no game.
As trivia would have it, the Street Fighter series, the Darkstalkers series, the Fatal Fury series, the Samurai Shodown series, and the first two games in the King of Fighters series have named normal moves for all characters. That being said, they’re pretty obscure (believe me, I’ve been looking!), and genuinely trivial for the most part.
Typically, they will be classified as follows. More often than not, they are abbreviated because the differentiation is important, but the descriptions are long-winded; however, there is no universally accepted abbreviation standard in English as far as I can tell.
Normal moves can usually be divided into ‘punch’ and ‘kick’. However, these are just button names and such; for example, plenty of boxer characters do punches when you hit a kick button, and there are hardcore dudes who will headbutt to the tune of the punch button.
And this is just if the game happens to classify the moves that way. More recent games have been willing to forego the traditional punch/kick divisions, and weapon-based games never really did use them because it doesn’t make much sense.
Mutually exclusive from the attack-type division, there is the division by strength of the moves. Capcom’s typical 6-button layout divides these into weak, medium, and strong buttons (also called light/medium/heavy punch/kick); these are usually abbreviated for sanity’s sake. The Tekken series has a left/right distinction; Mortal Kombat has a high/low distinction.
Some people prefer to call the buttons by name, which will only help one classify the move’s divisions if one knows the system beforehand (or if the names explicity list their faculties). The advantage to this, however, is that the names are more explicit this way.
In games like in theLast Blade series or Rival Schools series, there aren’t a whole lot of buttons to relate normal moves to.
There are things that are operated just like command moves, but because they come with most characters in more or less the same way, they are categorized as normal moves. Yes, simply because someone says so.