Understanding 〜出す and 〜出る compound verb pairs

Question

I noticed that there seem to be a lot of compound verb pairs that end in 〜出す and 〜出る.

Some examples:

• はみ出す／はみ出る
• 突き出す／突き出る
• 湧き出す／湧き出る

It's clear to me that for sentences that take a direct object, the 〜出す verb seems to be preferred:

• 窓から顔を突き出す✅
• 窓から顔を突き出る❌

However, in sentences where an intransitive verb is required, both the 〜出す verb and the 〜出る verb seem to be accepted with a similar meaning:

• 岬が海に突き出している✅
• 岬が海に突き出ている✅
• 天然水が地下深くから湧き出している✅
• 天然水が地下深くから湧き出ている✅

Therefore for these intransitive cases, I was wondering if there is any difference in nuance or meaning between the 〜出す and 〜出る verbs, and whether one tends to be preferred over the other?

Answer 1

岬が海に突き出している。

岬が海に突き出ている。

These two sentences describe the same scene. However, the one with 出る sounds more natural as an objective description to me. The one with 出す sounds a bit like the cape is sticking itself out of its own volition, giving the sentence a literary feel.

天然水が地下深くから湧き出している。

天然水が地下深くから湧き出ている。

The same thing can be said about this pair, but to a much lesser degree. The sentence with 出す sounds only slightly more dynamic. I get a feeling that the part of the scene where the water is coming out is zoomed in on. The difference is subtle, though. This is probably because water is expected to move on its own unlike a cape.