I don't know, but I think that you can use these verbs optionally, because according to my dictionary, "out" is in brackets. I don't know if there is a slight difference between these 2 verbs.
[intransitive, transitive] to have difficulty breathing or speaking gasp (for something) He came to the surface of the water gasping for air. gasp (something) (out) She managed to gasp out her name.
Couldn't be "She managed to gasp for her name"?
Gasp is normally, but not always, used intransitively. It means ‘to inhale or exhale convulsively with an open mouth, as a result of distress, exertion, surprise, etc.’. The phrasal verb gasp out is transitive and means ‘to utter with a gasp’. (Both definitions from the OED.)
She managed to gasp for her name is not grammatical. It has to be She managed to gasp her name or, perhaps more frequently, She managed to gasp out her name.
Two separate concepts:
So no, they aren't really interchangeable.
Gasp out is a phrasal communicational verb that means, roughly 'say, with sound effect of gasping'. So it's transitive, but that's because of the construction frame
[human sound/visual effect + direct/indirect dialog chunk] (+ out)
becomes a manner of speaking verb (or, quite often, phrasal verb):
[manner-of-speaking verb + direct/indirect dialog chunk]
followed, in the case of phrasal verbs like gasp out, by a particle ("intransitive preposition")
or by transitivizing prepositions to allow objects, like the ones in
Yell to George about the new quota.
There are lots of constructions that use these verbs this way, e.g,
In a construction like that, one needs no out, though it's usually OK:
I conjecture that whisper out is problematic because whisper is already a speech verb. What I'm calling "Speechification out" comes from the experience of emitting language, through various means, for various purposes, with various effects. It's a semantic addition to a human voice or facial or body communication effect that converts it -- if it takes [and it often doesn't, he winked] -- into a metaphorical speech verb.
Turns out how people talk is something people talk about a lot, and consequently it has lots of specializations in its language, like the English human motion verbs or verbs of cutting. Most are metaphors, and most are seriously context-dependent.
