I know both of them are categorized under aspect, but do imperfective refer to "was doing" and perfective refer to "have done"? Then how about "have been doing" and "is doing"? What do they belong to?
Different grammarians categorise things differently:
- In traditional grammar and many EFL/ESL courses, constructions such as the present perfect and the present progressive are called tenses (specifically, they are compound tenses or analytic tenses). In this scheme, the concept of aspect is rarely used or mentioned.
- In most modern grammar books, only the simple tenses (or synthetic tenses) are called tenses. There are two tenses - they are variously named the present and past, or present and preterite, or nonpast and past. Perfect and progressive are distinctions of aspect, not tense. On this view, the term "tense" is reserved for morphology.
- However, some linguists (while regarding the progressive as a distinction of aspect) see the perfect as a distinction of secondary tense (Huddleston & Pullum).
You have said that you regard the perfect as an aspect. On this basis, there is a distinction between perfect aspect ("I have done", "I had done") and non-perfect aspect ("I do", "I did").
The two aspects (perfect and progressive) can be present individually or both at once or both absent. In "I have been doing", the construction is progressive perfect, since the progressive and perfect aspects are both in use.
- Perfect: (to) have done, I have done, I had done.
- Progressive: (to) be doing, I am doing, I was doing.
- Progressive perfect: (to) have been doing, I have been doing, I had been doing.
- Non-perfect, non-progressive: (to) do, I do, I did.
(We could include "will have done" in the perfect list and "will be doing" in the progressive list, and this would be correct, but "will have done" is simply composed of the modal "will" plus the perfect form "have done", so it is no more a distinctive form than "might have done", "could have done". The modal "will" is not regarded by most linguists as forming a distinct tense.)
The progressive aspect is sometimes called the continuous aspect. For someone familiar with (say) French grammar, it may be tempting to refer to the progressive as the imperfect. But this would be incorrect, because the perfect and progressive can be combined, as we've seen.
Some grammarians have called the perfect/non-perfect distinction "perfective"/"imperfective", but most people regard the use of the term "perfective" for aspect as confusing. The reason is that other linguists use the term "perfective" to refer to verbs that express a completed action - and on this basis, the simple past is also often perfective. So, the perfect aspect should be called "perfect" and not perfective.
English has a group of "perfect" tenses. They are formed in a similar way to the perfect tense in Latin or French with an auxiliary verb "have". But the meaning is different. The perfective in French indicates actions completed in the past. The perfect in English means states resulting from past actions continuing to the present.
English doesn't have an "imperfective". There is a past tense for describing actions in the past.
There are also a set of continuous verb forms (also called "progressive"), These are made by combining a "be" verb with a present participle. They indicate actions that are extended in time, or repeated, or temporary.
Continuous forms can be in present or past tense, and can be combined with perfect to give a "present perfect continuous"
So, there is no imperfect. The perfect tense has a different meaning to the similarly name tense in Latin and Latinate languages. The "be ...ing" forms are called "continuous".