Sentences excluding "being"

I am wondering about a certain type of sentence construction which seems to somehow exclude the word being. For example,

A native English speaker, he was well suited for the task.

Well versed in the English language, he was well suited for the task.

These are different in essence: the first includes the noun in the first sub-clause and the second does not. Are any or both of these grammatically sound?

You're right, they are grammatically different.

The first uses a NP (noun phrase) in apposition to the subject.

The second uses a AP (adjectival phrase) modifying the subject.

Both are fully grammatical, though many people would, as you suggest, transform them to different kinds of constituent: either an absolute clause (some would say a modifying clause) with "being" or (in the first case) an adjunct PP (prepositional phrase) with "as".