Are there any differences between the following two sentences?

Both of your sentences mean the same. In this context no Native English speaker would think that "around the fire" would mean that the men avoided the subject of the fire. The sentence obviously means that the men were sitting around the fire and chatted.

Both forms are normal in British English. As Oldprof says - there are often several ways that any idea can be expressed in English. In some case one form or another feels more natural in British or American (etc!) English.

Both are good. There is a lot of lee-way in the English language. One of the reasons even foreigners often choose English to write their pieces. We can also write:

The old men sat round the fire and chatted.

Sentence 1 gives equal weight to sitting and chatting. Sentence 2 gives more weight to sitting and less to chatting. My example is like 2 in this case.

The weight of an idea within a sentence is typically indicated by the number of words associated with that idea. The more the words, the more important, the more weighty, is that idea.

While both convey the same scene, the 2nd is a better sentence. It is not as wordy. The first sentence seems worded awkwardly. A better sentence would be "The old men chatted as they sat around the fire."

You need to write 'round" properly, as a contraction, WITH the apostrophe. If you use the second version, you need a comma after "fire".

The second version is preferable to my ear because, presumably, the men were, first and foremost, SITTING around the fire.

There is little difference. Just an alternative way of saying the same thing.

You could also say, the old men sat round the fire and chatted.

They are both technically correct--NOW. Older rules dictated that you should not end sentences with prepositional phrases (such as, "round the fire"), but that rule has seemed to lose it potency in the last few decades. (I just did it there! I see why it's not the hard and fast rule anymore.) For the real sticklers, 2 would be the more technically correct version.

"chatted round the fire."

This implies that the fire was between them, an obstacle, which is subtly different from sitting around the fire.

We talked around a subject means we avoided the subject. "Chatted round the fire," means your chat avoided the fire.

Oh and the proper way to spell this is either around or 'round, if you prefer dialect.