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).