"Continuous" vs "Discontinuous" verbs: What to call them in English and Japanese?

Question

On my trip home today, I was thinking about how うちに帰っている would be incorrect for my current situation, as I'm currently travelling home and not already at home. I'll walk through my thought process from here:

Consider 食べる:

食べる - I will eat

食べた - I ate (without proper grammar, "I eated")

食べている - I am eating

Often 帰る is translated as "to return", but copying the same transformations from the 食べる case is incorrect:

帰る - I will return

帰った - I returned

帰っている - [WRONG] I am returning

If we instead translate 帰る as "to be returned" (where "returned" here is intransitive), we still get proper meanings:

帰る - I will be returned

帰った - I have been returned

帰っている - [CORRECT] I am returned

So, I wondered if this was the case that all transitive verbs were "continuous" and all intransitive verbs were "discontinuous", but this is not the case: かぶる is transitive and "discontinuous", and 泳ぐ is intransitive and "continuous":

かぶる - I will don it

かぶった - I have donned it

かぶっている - I am (being donned) it

泳ぐ - I will swim

泳いだ - I have swum

泳いでいる - I am swimming

So my next question was "is this strictly an English phenomenon?". Rather, am I fixing a problem that only really exists in English by adding "to be" onto definitions?

Consider this timeline of 食べる:

食べた happens after 食べている, that is, 食べている describes the interval before 食べた.

This is not the same of 帰る:

帰っている describes the interval after 帰った. So, this is not strictly an English phenomenon to my understanding.

So, is there a name for categories A and B? Especially a name for them in Japanese?

	A	B
Transitive	食べる	かぶる
Intransitive	泳ぐ	帰る

Answer 1

The Japanese terms you are looking for are 継続動詞 and 瞬間動詞. 継続動詞 refers to verbs whose -teiru forms typically refer to progressive actions, whereas 瞬間動詞 refers to verbs whose -teiru forms typically refer to resultant states. 瞬間動詞 is often called a punctual verb or an (instant-)state-change verb in English.

I said "typically" because the vast majority of verbs actually work in both ways. 家に帰っている safely means either "I'm on my way home" and "I'm already at home" depending on the context. The same is true with 食べている and 寝ている (see: Is 寝る a stative or active verb?). It's perfectly fine to say もうお昼を食べていますか "Have you already eaten lunch?". There are expressions which force either progressive or stative readings (e.g., ～ているところ forces a progressive reading, and 過去に3回～ている forces a stative reading).

As you said, transitivity has nothing to do with the aforementioned categories. For example, 始める (transitive, "to start something") and 始まる (intransitive, "something starts") are both nearly always punctual verbs (会議を始めている "We have (already) started the meeting" vs 会議が始まっている "The meeting has (already) started").