Communication Accommodation Theory (CAT) (see wikipedia page) is when people change their speech to either sound more like their interlocutor (convergence) or less like their interlocutor (divergence). Suppose a British person moves to the US and wants to sound more "American" so that she can fit in, sociolinguists would say that she is accommodating to the new American dialect or converging. Moreover, suppose an American moves to the U.K, but doesn't want to seem "British" so he exaggerates his American accent, in this case he is not accommodating, he is diverging. CAT is really complicated and has to do with many complex factors like identity and social networks.
Sociolinguistic prestige, (see wikipedia here) on the other hand, has to do with the value that speakers in a certain speech community give to a specific way of speaking. Overt prestige is like prestige "out in the open" which is usually given to the variety spoken by the by people with socioeconomic resources in a given speech community (like RP in British English). Covert prestige refers to the fact that even though a certain way of speaking in a speech community is widely stigmatized, some speakers may indeed find solidarity with those ways of speaking. For example, it's well known that Spanish is a stigmatized way of speaking in the United States (see Ofelia García), however, in certain situations in the U.S, by speaking Spanish, it may be advantageous, like at a party with other Spanish-speakers, in this situation, we would say that Spanish has covert prestige. You can also think about prestige for specific sociolinguistic variables (like the "r" in Lavov's 4th Floor Study)
These terms are quite different. CAT is more of a micro phenomenon referring to the actions of individuals, while prestige has to do with the attitudes of speech communities. Though they can be used together, for example, many individuals either converge or diverge to the prestige variety in a given speech community.