I think you have your terminology a little out. The wicket is the combination of the three stumps and the two bails - it's what the bowlers are aiming at. I've not heard of the term "square" used in cricket before although I gather that it can be used, but the area where the wickets are is traditionally called the crease. This area can also be called the pitch (pitch does not refer to the whole playing area) whereas the field is the entire playing field.
Cricket has slightly different terms (as above), largely because cricket - not football - is the origin for most British sports terminology, and the other terms we now view as being "typical British terminology" are actually old cricket terms which have been misapplied to other things (i.e. the way that the "pitch" which is merely the most important area of a cricket field now being used for the entirety of other sports' fields of play.
The other notable exception is the "jersey/kit" term for cricket. Cricket is practically unique in British sports as its' the only sport where people wear armour for protection. Because it's immediately obvious at any time which players are on each team (the "attacking" team are the only ones holding the bats, and they also have very distinctive protection) then there's no real need for the two teams to wear different clothing. The concept of different teams wearing different colours is a very recent development. Traditionally both teams would play in white and the only difference would be the club badge on their t-shirts. For this reason, terms are very rarely used to talk about the "kits/shirts/jerseys" being worn, because they simply aren't relevant to the game. They're not really the kinds of things that fans buy to wear to games.
