Taka said:
So, what kind of difference do you feel in their meanings when you hear those sentences?
(a) There is a crying baby.
(b) There is a baby crying.
Sentence (a), as is, doesn't make sense to me. It'd make more sense if a location were added, like this,
(a) There is a crying baby
on the bus.
As for the semantic difference between (a) and (b), one exists. Structurally (a) and (b) are different. That difference tells us they are also semantically different. Now that doesn't mean to say they are drastically different in the meaning they express. Let's look at the data:
(a) There is a crying baby on the bus.
==> 'crying' functions as a participle, specifically, a nominal participle (i.e. an adjective), and as an adjective it describes the noun 'baby. It tells us what kind of baby it is.
(b) There is a baby crying.
==> 'crying' functions as a participle, specifically, as part of an omitted phrase (i.e. who is),
(c) There is a baby
who is crying.
(d) There is a baby and
it is crying.
Both (c) and (d) mean, "There is a baby crying."
The difference between (a) and (b) is this. 'crying' functions as a nominal in (a)--that is, it describes a noun, a thing--and functions as a verbal in (b)--that is, it describes an action. There's a difference between a nominal participle and a verbal participle.
Compare,
(e) There is a
big box on the bus. (Adjective)
(f) There is a box that is
big on the bus. (Adjective)
(g) There is a box
big on the bus. (Verbal Participle)
Sentence (g) is ungrammatical because the adjective 'big' cannot function as a verbal participle. It needs a subject (i.e. that) and a verb (i.e. is); 'that is' cannot be omitted.
But with verbal participles, the subject and the verb are often or rather regularly omitted,
There is a baby
who is crying on the bus.
There is a baby crying on the bus.
Gerunds are examples of verbal participles that function as nouns:
She likes
swimming. (Noun)
Adjectives that a) modify a noun and b) follow the noun are examples of verbal participles that function as adjectives,
There is a baby crying. (Adjective)
In sum,
(a) There is a
crying baby on the bus.
==> 'crying' describes the (kind of) baby. (Nominal)
(b) There is a
baby crying.
==> 'crying' tells us what the baby
is doing. (Verbal)
===
All you guys
(who are) partying way past their prime are old.
The relative clause '(who are) partying way past your prime' functions as an adjective modifying 'guys'. Within the relative clause we have a participle 'partying', which is semantically connected to the verb BE (i.e. are). As part of the verb BE, an -ing word functions as a verbal participle, and as such it refers to an action.
All the best,