grammaticality - Do the -ing and to-infinitive "verbs" that follow catenative verbs always take the grammatical function of "noun"?

I'm wondering whether or not the verb form that follows a catenative verb has the grammatical function of a noun or of a verb, and whether or not it depends on the first catenative verb.

"I like to run"
"I like running"

the -ing and the to infinitive can easily be switched in this sentence, and it seems to be implying "I like [the act of[running]]", so both the infinitive and the gerund are nouns.

"I like to run marathons"/"I like running marathons"

These seem like they might still be nouns but need "verb powers" to take the object, and then these sentences really turn into "I like [the act of [running marathons]]"/ "I like [to be in the state of [running marathons]]".

Is this true for both the -ing (and so it would be a gerund) and the to-infinitive? Are they, sort of, initially verbs so that they can take the object, and then the verb + object becomes a noun phrase?

If this is true, I'm also wondering if the same rules apply for a catenative verb such as "start".

"I started to run in the mornings"
"I started running marathons in 2008"

"start" is a catenative verb that isn't a cognitive/emotion verb, and specifically suggests action. So what is the grammatical function of the to-infinitive and -ing verb forms? are they verbs? are they nouns? It just seems incorrect to say that their grammatical function is a noun, but everything I've seen on the internet is pretty vague. I've also seen that to-infinitives are never verbs, but only from one source and it just doesn't seem right to me.

So any ideas on the true grammatical function of the -ing and the to-infinitive after a catenative verb? And is it universal across catenative verbs, or does it depend on the verb category?