Is adaptive security the same as full security?
I don't know what you mean by "full security", but "adaptive" just means that the oracle queries from the attacker depend on the results of previous queries. In contrast, "non adaptive" means that the attacker simply makes all the queries in batch, that is, without adapting his queries from previous results.

Update: based on the paper from your comments, it seems that "full security" is opposed to "selective security". Both "full" and "selective" security are defined in Chapter 2.3.3 of that paper. According to that definition, both models are adaptive, since queries from Phases 1 and 2 are adaptive.