1. I find the term Present Participle can be misleading. E.g. The Past Continuous tense = Past of Be + Continuous Participle (correctly saying in-progress then). But if = Past of Be + Present Participle, there's nothing "Present" about this tense.

2. It's just a personal preference. Same goes for the Perfect Participle vs the Past Participle when it comes to, say, the Present Perfect tense.

3. I use my preferred terminology to separate on the one side PRESENT, PAST and SHALL/WILL/WOULD, and on the other side the INFINITIVE and the participles CONTINUOUS and PERFECT. This distinguishes between TIME and ASPECT which constitutes a compound tense.

4. I find (3) useful esp with the compound tenses: first Auxiliary (Present/Past/Shall/Will/Would) + second Auxiliary (if any, BE/HAVE/BEEN) + third Auxiliary (if any, BEEN) + Main Verb (Infinitive/Continuous Participle/Perfect Participle)