Hockey players are careful but they still get hurt often

Question

I was studying sentence patterns and I came across the following sentence in a mini test after the explanation on the same website.

4. Hockey players are careful but they still get hurt often

The site labels the sentence as compound but I have a sentence in my book which is labelled as simple which is the following:

She cooks very well and has a lovely cafe.

I can understand the sentence in my book why it is a simple sentence since the subject is related to two verbs, which is called compound verbs.

But I cannot understand the sentence in the test which I think it seems to have similar pattern that one subject, players, and there are two verbs, be and get .

If the website is correct ( the sentence is compound) , is it because the verbs have different tenses and types..

Can we make the sentence simple but only changing verbs?

For example:

Hockey players are exhausted but they still are careful.

Hockey players play carefully but they still get hurt often

Are they now simple?

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Another reason for asking this question is I become mostly unsure if I should add the subject again after the conjunction.

For example: In the answer of @Nothing at All the sentence "She cooks very well and has a lovely cafe" is separated as

She cooks very well . and has a lovely cafe.

In this case " and has a lovely cafe" is obviously incomplete.

But I am a bit concerned if it is grammatically %100 wrong if I write the sentence by adding "she" after conjunction as in the following.

She cooks very well and she has a lovely cafe.

or if I omit "they" as in the following

Hockey players are careful but still get hurt often.

Answer 1

EDIT: Removed the first part of my answer. (The entire answer becomes too long)

There is nothing wrong with transforming sentences the way you explained.

Hockey players are careful, but they still get hurt often

is equally correct as

Hockey players are careful but still get hurt often

Assume the following (simple) structure of a sentence:

S + P, SC + S + P.

Where S, P, and SC represent Subject, Predicate, and Subordinate Conjunction respectively. Adverbs, adjectives, modifiers, and other parts of speech can be added to this sentence without making it grammatically incorrect, but they are not to be worried about now.

Removing the comma, and the subject of the second clause, you're left with:

S + P + SC + P

The "P + SC + P" will together form a compound predicate, and therefore what remains is a grammatically correct sentence. e.g.

Elise eats, and she swims.

becomes

Elise eats and swims.

The same can be shown for transforming a simple sentence into a compound sentence. The only thing you need to take care of is punctuation, and what you add.

She cooks very well and has a lovely cafe.

becomes

She cooks very well, and she has a lovely cafe.

Answer 2

It's a compound sentence because without 'but', both parts of the sentence could stand on their own.

Hockey players are careful. They still get hurt often.

Compared to your example:

She sings well. And has a lovely café.

The second sentence is incomplete, thus the sentence

She sings well and has a lovely café.

is simple.

Both of your hypothetical sentences are compound:

Hockey players are exhausted. They still are careful.

Hockey players played carefully. They still get hurt often.

The second seems a bit strange, though, because the tenses don't match.

Answer 3

The website is correct. The example "Hockey players are careful but they still get hurt often" is compound not because of what it means, but because of its form. It contains two sentences, "Hockey players are careful" and "They still get hurt often". The term "compound sentence" is grammatical, not semantic.