terminology - Is there a better term for "perfect infinitive", "perfect participle" or "perfect gerund"?

BACKGROUND

There are grammar terms such as 'present perfect' and 'past perfect' as in:

She has learned English for 10 years. [present perfect]

She had learned English when she was little. [past perfect]

I believe that these terms are fairly well established in more recent grammars as well as in the traditional grammar.

The way these terms are made is such that the first word 'present/past' represents the tense of the auxiliary 'have', and that the second word 'perfect' the structure of 'have + past participle'.

Now, I notice that the term 'perfect infinitive' is used in the traditional grammar to refer to the form 'have + past participle' where 'have' is in the form of infinitive.

For example:

She seems to have learned English when she was little. [perfect infinitive]

Similarly, the terms 'perfect participle' and 'perfect gerund' are used to refer to the form 'having + past participle' where 'having' is in the form of participle and gerund, respectively, as in:

Having learned English, she now wants to learn Chinese. [perfect participle]

They are not aware of her having learned English when she was little. [perfect gerund]

ISSUE

I don't know whether--or how well--these terms 'perfect infinitive', 'perfect participle' and 'perfect gerund' are established among more recent grammars, but they just don't make sense especially when you consider the other terms 'present perfect' and 'past perfect', where the first word represents the tense of 'have' and the second word the entire form 'have + past participle', because it's the other way around in the terms 'perfect infinitive', 'perfect participle' and 'perfect gerund', isn't it?

QUESTION

So I'd like to know first if anyone agrees with my confusion as to these terms being inconsistent, and secondly if better terms are actually in use for these latter three.