"pseudo-", "quasi-" "semi-" and

Pseudo- comes from the Greek for false/lie and refers particularly to something not genuine.

Quasi- comes from the Latin for almost and refers to something that is almost something else.

Semi- is the Latin for half and refers to something that is half-something else

In late usage, however, all three have been used to mean sort-of-

As others have said, pseudo = false, quasi = almost, semi = half.

In engineering and science, these tend to have fairly technical meanings. That is, a pseudopod is something that looks like a foot but is not, semiannually means twice a year (and I can't really think of an accepted repeatable term that begins with 'quasi').

In mathematics, however, all bets are off. A semigroup is like a group and has fewer defining properties than a group, but in no way is it anything like half of a group. Similarly a quasigroup. (this is a general notice about mathematical terminology, the inventors of the terminology usually have some metaphor in mind when the technical term is chosen, but that metaphor hardly ever translates to anything meaningful).