A phrasal verb is a verb combined with a preposition, an adverb, or an adverbial particle, all three of which are by their very nature uninflected.

A phrasal verb is also called verb-particle construction, verb phrase, multi-word verb, or compound verb. American English expressions are two-part verb or even three-part verb.

Table of contents
1 Idiomatic or literal verb-particle constructions?
2 Grammar in literal verb-particle constructions
3 Examples of literary and idiomatic verb-phrases
4 The origin of idiomatic phrasal verbs

Idiomatic or literal verb-particle constructions?

Some grammarians claim that only the figurative, idiomatic or metaphorical usage of the combination should be called a phrasal verb, and that the literal use, where both the verb and the preposition are analysed, and both are found to have a literal meaning in a phrasal context, should be called verb and particle or verb-particle constructions.

Other linguistic experts are of the opinion that all verb-particle constructions in both literal, as well a figurative/idiomatic use should be called phrasal verb, irrespectively whether they have an individual meaning or not.

Emphasis in idiomatic phrasal verbs is put on the analysis to ascertain whether either verb or particle have a meaning. If neither component has a meaning of its own within the context of the sentence, it confirms the idiomaticalness of the whole and all that needs to be noted is whether the idiom is valid and recognised as such.

Grammar in literal verb-particle constructions

Literal verb-particle constructions on the other hand necessitate much closer attention to syntax, because as both components have a meaning, the composition of the whole sentence has to be much more precise to have the actual meaning and function of each word within the syntax confirmed rather than the user being able to rely on a known idiom.

So it is, that grammatical and syntactical points in literal verb-phrases are much more important than they are in idiomatic phrases, where the known idiom determines the structure.
Is the transitive form separable or not, for example, as in hammer a nail in or hammer in a nail, where the particle precedes or follows the object in so-called 'particle shifts'?.
Is the particle preceding or following the object as in these examples: be something in... or be in something, etc., in this way changing the meaning entirely?

Literal verb-particle constructions are of a much more open type than idiomatic constructions. Every time a (new) situation is described with a literal verb-particle phrase a new form may automatically be created.
The phrase to go to... alone will form as many literal verb versions as there are geographical entities globally, as in to go to New York; to go to Honduras; to go to the UK, etc.

On the other hand idiomatic phrases are certainly finite in number. Idioms tend to be well-established in the English language, having been created probably as a metaphor, and now being used as a handy standby as and when required. However, they have to be recognised as being valid as idioms. That does not mean that new idiomatic verb phrases may not be created.

A more recent example has been, of course, to chill out. It is a metaphor and because it is used so often these days, it has become an idiom and a cliché.

Examples of literary and idiomatic verb-phrases

Many phrasal verbs may, of course, be used either in the idiomatic  or the literal sense, such as:

He came across the garden to speak to me (literal)
I came across an old photograph (idiomatic)
We came across him while he was working out (idiomatic)
The old lady came across as being very frightened (idiomatic)

or even: I am trying to keep my head above water, in the sense of keeping out of debt, which has an idiomatic meaning;
or
I am trying to keep my head above water, in the literal sense of not drowning.

The origin of idiomatic phrasal verbs

Originally all idiomatic phrasal verbs almost certainly started out as a verb and particle in literal usage. Just as a picture hangs on the wall, or we cross over to the other side of the road, so a mother may have taken a last look at her child going off to school, or may in fact have "looked after" the child, a usage whose meaning has changed in that it describes an entirely different activity in the modern context to look after (someone) meaning to ''care for someone.
However in everyday life an idiomatic phrasal verb too, like any other grammatical constructs, becomes fixed and authentic enough in time by its being used frequently.