At least as far as the standard Russian linguistics go (i.e. as most of us learned in 5th grade), there are perfective and imperfective verbs, not forms of them.
It does mean that a lot (most?) of the Russian verbs do not have a present tense for example. I think it is still more natural to stick to this convention rather than to what is taught in many Russian as a second language books, that is, picking one perfective verb, closest in meaning to an imperfective one, and calling it a form of the other.
The reason is that it is not always a 1-1 correspondence, and furthermore, any prefix you add to a verb will change its meaning a little bit.
But it is true that the "perfectiveness" functionality is typically expressed by tenses in other European languages. My French is not too good, but it is similar to the difference between "I was writing a letter" and "I have written a letter" in English. In Russian we only have 3 (and for some verbs, 2) verb tenses, instead of something like 12 in English, so there is another way of doing the same thing.