I understood your question as asking whether different constructions are used to express the ideas of
A and B are different
and
X and Y are different
where the statement
A and B are different in X and Y
is true.
If my understanding is correct, I find it to be a very interesting question.
Your English sentence, which is actually two sentences connected only with a comma, can be translated as:
沖縄と北海道は違います。気候と桜の咲く時期が違います。
And these can be combined into one sentence, as below:
沖縄と北海道は、気候と桜の咲く時期が違います。
Actually, 気候や桜の咲く時期 sounds more natural than 気候と桜の咲く時期 because there must be other things that are also different, not just those two. However, let’s use と here so we can focus on the main difference, which is that of は and が.
Although I cannot say for sure this is a definite rule, I think that, unless A (沖縄) and B (北海道) appear in a subordinate clause, they usually don’t take the subject’s spot with the subject marker が in a sentence with 違う. That spot seems to be reserved for X (気候) and Y (桜の咲く時期), which are properties in which A and B differ.
Here is an example where A and B appear in a subordinate clause:
沖縄と北海道が違うのは、気候と桜の咲く時期です。
は may be used with X and Y to emphasize the difference in them in contrast to similarity in other aspects of A and B.
沖縄と北海道はどちらも人気がありますが、気候と桜の咲く時期は違います。
By the way,
沖縄と北海道は、気候と桜の咲く時期が違います。
sounds a bit like it is meant for someone who already knows Okinawa and Hokkaido are different in some way and wants to know what’s different. In other words, the information conveyed by the first of the two original sentences is assumed to be already known.
If this is a problem, you could add で, as follows:
沖縄と北海道では、気候や桜の咲く時期が違います。
This で limits the scope of comparison to Okinawa and Hokkaido before the sentence goes on to state what’s different between them. It makes no assumption about the listener’s prior knowledge about Okinawa and Hokkaido and therefore works for anyone.
Lastly, although grammatically perfect, these sentences contain a logical issue inherited from the original English sentence. The reason why the time cherry blossoms bloom is different is precisely because climate is different. But that’s a different issue…