OCD is often seen alongside Asperger's, and, from what I've heard, conditions like these generally tend to come bunched together. (I took five psychology courses in my first two years of post-secondary -- that's the limit of my expertise.) I agree with the others who've found your therapist's drop-and-switch approach to diagnosis somewhat odd.
I'm diagnosed with both OCD and Asperger's. The part I think of as OCD includes repetitive checking routines (doors, taps, appliances, etc.), occasional unwanted thoughts and an urge to do things in patterns or "fours." For instance, on a checkered floor I usually feel compelled to move like a knight in a game of chess. The Asperger's, I think, is a matter of social and sensory weirdness, obsession (as an interest, not a bothersome fixation of the kind seen in OCD) and so on.
I'm not trying to give you my life story or anything, just some insight into your own condition. If none of what I've said applies to you, ignore it. But if you have significant numbers of symptoms of Asperger's and OCD, I think you should be skeptical of your therapist's recommendation to drop one diagnosis in favour of another.