Quote Originally Posted by Valda View Post
The word подойти is future.
No, it is not. It is the infinitive form, and the infinitive form does not have any grammar tense.
But it has the aspect: "подойти" is a perfective verb (as bitpicker noticed).

Perfective verbs are never used in present tense, they only have two tenses: past (e.g. он подошёл) and future (e.g. он подойдёт).

Quote Originally Posted by Valda View Post
"I will approach/he will approach/they will approach/.... etc etc
I will approach - Я подойду (perf.) and Я буду подходить (imperf.)
He will approach - Он подойдёт (perf.) and Он будет подходить (imperf.)
They will approach - Они подойдут (perf.) and Они будут подходить (imperf.)
etc.etc.

Quote Originally Posted by Valda View Post
"Now, we also got "подходить" - which means the same thing, but in present form!.
No.
1. It does not mean the same thing: "подойти" is perfective (a single completed action as a whole), but "подходить" is imperfective (it can be habitual, repeated action, or a single action in its process).
2. "Подходить" is not the present form! It is the infinitive form.The infinitive cannot have any grammar tense.

The imperfective verbs (unlike perfective ones) can form all 3 tenses: present (e.g. он подходит), past (e.g. он подходил) and future (он будет подходить).

Quote Originally Posted by Valda View Post
"Both of those verbs have past forms.
Yes. And both of them also have future tense forms.

Подходить:
present: он подходит, past: он подходил, future: он будет подходить
Подойти:
present: none, past: он подошёл, future: он подойдёт

Quote Originally Posted by Valda View Post
What's the difference between the past form of подойти and the past form of подходить then?
The difference is the perfective/imperfective aspect.
Valda, are you familiar with the concept of Russian aspect?