Talk radio is either the fertile valley or the fruited plains of popular speech. As a regular listener to several genres I have noticed both hosts and listeners confusing these two words: quasi and pseudo. One may almost understand why there might be confusion. At the very outer edges of the meaning of both they almost touch but they are distinct words with distinct senses. According to the Oxford English Dictionary the adjective pseudo comes from the Greek adjective ψευδής (pseudēs) which, according to Liddell and Scott,  means lying or false. In Greek the root ψευδ— (pseud—) was used as a prefix just as we do in English. Liddell and Scott give to interesting examples: ψευδο-δῐδάσκᾰλος (pseudo-didaskalos; false teacher) and ψευδο-κῆρυξ (pseudo-kērux); in Sophocles a false herald but in Christian usage a false preacher.This is a significant adjective in New Testament usage. In his catalogue of hazards, Paul says that faced danger from rivers, robbers, his own people (Jews), the city, wilderness, the sea, and from false brothers (ψευδαδέλφοις; 2 Cor 11:26), i.e., those who pretended to be Christians but who, in reality, were not and who put his safety or life in jeopardy. In Galatians 2:4 he complains about “false brothers” (ψευδαδέλφους) who pretended to be Christians but were really Judaizers, who were looking for an opportunity to accuse him (and others) for not keeping the Old Covenant (Mosaic) ceremonies and imposing them on the Gentile Christians.
Thus, the correct usage of pseudo is a substitute or a synonym for false. “She put on her pseudo-lashes and went out for the evening.”

On one of the sports-talk podcasts to which I listen (for just the slightest tidbits about Husker football) one of the hosts described an athlete who was capable of playing more than one position with the adjective pseudo. The adjective he should have used, however, was quasi, which, in distinction from pseudo is Latin. It signals “as if” as though. It also has the sense of nearly or almost. So, it is not difficult to see how one might confuse quasi and pseudo but they should be substituted for each other as if they mean the same thing. They do not.

The sentence, “He is a quasi-running back. He could play H-back, tight end or even full-back” does not have the same sense if we substitute pseudo: “He’s a pseudo-running back. He could play H-back, tight end, or even full-back.” A pseudo-running back would be a player who pretended to be a running back but was actually the quarterback. If Husker quarterback Tommy Armstrong lined up as a running back, he would be a pseudo-running back, since he is quarterback pretending to play another position in order to deceive the defense. Nebraska tight end Cethan Carter, who is quite capable of running the ball as an H-back, is a quasi-running back since he is not a full-time running back and since he ordinarily lines up at tight end.

So, use quasi when you want to say as if, almost, or sort of. When you want to say false or pretending use pseudo.