Basking is following a train of thought, not consciously. Oh, I remember how I won that math, I can squeeze some more pleasure out of that! The thought just comes to my mind, and I make no effort to push it away.
Savoring is consciously extending the pleasurable effect of something. It is inherently reflective: let me try to have a happier life by thinking of happy things. It is conscious in choosing the objects to savor: instead of what comes to mind, or what is most intense, what would my whole character benefit from? For example, it’s more useful if I savor a friendship - appreciate what my friend did for me even when I don’t feel it on a gut level - rather than bask in the memory of sex. The first brings reason and feeling closer together. The second usually doesn’t. (I don’t mean to be sex negative - but sex isn’t correlated with character.)
Another test: at the end of basking, there is a negative emotion. It’s like you’re trying to squeeze all the pleasure out of something, and the moment that it stops is sadness. Basking is dangerous, like having a tasp. Savoring decays smoothly to baseline.