Learn English – ‘If’ conditional – present tense vs future tense

Traditionally, it is considered neither, though it is sometimes called a mood for lack of a better word. The word function would seem the best term. I am assuming that you are talking about the word would in your example. The adjective "conditional" just means "related to a condition"; when used as a noun, it usually refers to a function of the past subjunctive tense of modal verbs (would, could, might, and should).

There are three traditional moods in English, indicative, subjunctive, and imperative; there are several tenses, which are combinations of moods, aspects, and temporal properties (you might say past and present are aspects, though they are usually not so called).

There are three types of conditional sentences, as Henry has pointed out, which are mainly just sentences in which an explicit or implicit condition is present. There is a function of the past subjunctive that is called conditional because it is used with one of these types, the so-called hypothetical condition (if he were rich, he would be unhappy). I think that is the one you mean; while it is sometimes called a mood, I find this unclear and confusing: how can something be of two moods, both subjunctive and conditional? Function is the term that both fits best with established terminology and best describes what kind of phenomenon it is.

I'm afraid conditional sentences in English have nothing or next to nothing to do with the sequence of tenses in 'time line'.

a. When you're talking about some possibility in the future, you use present simple in conditional and future simple in main clause.

If you hand in your report tomorrow, the teacher will forgive you.

b. When you're talking about something, happening at the time of speaking, then you use past simple in the conditional and future-in-the-past in main clause. My English language teacher called this kind of conditional "next to impossible" - maybe, just maybe the conditional is fulfilled and the main clause then will take place.

If he handed in his report, the teacher would forgive him.

Meaning that he, whoever he is, can amend whatever transgression he made by handing in his report no later than the time I said this phrase.

c. When you're talking about something in the past, then you use past perfect in conditional and future perfect in main clause. By analogy, it's an "impossible" kind of conditional - something already didn't happen, but if it happened when it should have, then...

If he had handed in his report yesterday, the teacher would have forgiven him.

He didn't hand in his report in time, and lost any chance of being forgiven.