The experience of MS can be very different for everyone. Even people with the same sub-type can have a completely individual set of symptoms. So no, I don't think having different symptoms means two people could not have the same type of MS.
However, there are some other indications yours probably wouldn't be PPMS, because you mention that you have got better - albeit not completely.
Whole body symptoms, resolving to just the hands, is quite a significant improvement.
Usually, with progressive types of MS, there isn't this pattern of flare-up and recovery. It just gets worse (but not always quickly).
Don't be mislead by the idea that always having some symptoms means it's automatically a progressive type.
Even though it sounds contradictory, relapsing remitting is still a "progressive" disease. Although complete recovery from attacks (relapses) is possible, especially in the early days, many people find there is residual damage that never completely resolves. So being in remission doesn't necessarily mean you feel fine, and have no symptoms! It just means you're better, compared to how you were when you were having the relapse.
For example, I always get painful feet now. This is due to permanent damage. But during a relapse, I couldn't feel them at all. So although there's been some improvement (sensation returned), everything's not 100% OK.
Any degree of recovery suggests a relapsing remitting course. It needn't be complete.
As an aside, as much as MS varies, I'm very surprised anyone with a confirmed diagnosis hasn't had at least some "weird sensory symptoms", as these tend to be very much a feature of the illness, even though everyone might get their own individual type of weirdness.