"I sat in the kitchen sipping my coffee" AND "… and I was sipping my coffee"

Question

"I sat in the kitchen sipping my coffee"
"I sat in the kitchen and I was sipping my coffee"

These two sentences are the same meaning, but what type of grammar are between these two sentences?

Answer 1

I was sitting in the kitchen (and) sipping my coffee

This is in the past continuous, the two actions were both in progress at a specific point in the past.

The OP's first sentence:

I sat in the kitchen [while/and I was] sipping my coffee.

The first verb is in the simple past, and suggests a more enduring action than the second, sipping, which is in the present participle. In this example, the conjunction (while OR and), the subject (I), and the auxiliary be (was) have been omitted. Ellipsis is used when predictable words are non-essential to meaning.

Answer 2

OP asked about the grammar of the following sentences:

1. "I sat in the kitchen sipping my coffee."
2. "I sat in the kitchen and I was sipping my coffee."

In the first sentence, "sipping my coffee" is a participle phrase functioning adverbially, modifying the verb "sat" and it indicates a simultaneous action.

Example.
"Hands shaking, I sat down to take the test.".
("Hands shaking" consists of a noun and a participle, modifying the entire main clause.)

The second sentence is a compound sentence with two independent clauses joined by "and".

Answer 3

I sat in the kitchen sipping my coffee.

I sat in the kitchen and I was sipping my coffee.

Edit

The two sentences are of different constructions. The second is an unnecessarily complicated way of saying the first one.

The first sentence has I sat in the kitchen as the main clause; sipping my coffee is a gerund-participle phrase (or clause) describing the manner of sitting.

The second sentence has two equal clauses joined by the conjunction and. I would add a comma:

I sat in the kitchen, and I was sipping my coffee.