Would both of these sentences be correct? Do they both have the same meaning?
たくやの後ろに彰が座っています。Akira is sitting behind Takuya.
彰はたくやの後ろに座っています。Akira is sitting behind Takuya.
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They are both natural-sounding Japanese sentences, given the right context, so they are both 'correct'. Whether or not they have the same meaning depends on how you define 'meaning'. Do they describe the same state? Yes. Are they interchangeable for each other? Very much no.
The difference regards how the information is presented - which part is information the listener already knows, and which part is the information the sentence is meant to convey. The difference is marked partly by word order (a thing I'm pretty sure all natural languages do) and partly by Japanese's role-marking particles*.
First, let's break the sentence up into subparts:
Your first sentence orders them like this:
[たくや] の後ろに [彰] が [座っています]
In this sentence, 彰 is placed second, and additionally marked with が - both of which indicate that it is the focus of the sentence†. This means that 彰 is being presented as new information - we haven't been talking about him before. たくや is placed first, suggesting he's the topic - he's been mentioned already. (He's not marked for topic with は, probably because that would sound more like contrastive topic, where we've talked about what's behind someone else and now we're talking about what's behind たくや.)
This sentence sounds like it could be introducing 彰 as a new subject for discussion (you could imagine this being the introduction sentence for a new character in a book - we've mentioned his friend たくや, now we're focusing on him himself). Alternatively, it could be the next entry in a list of people sitting in rows - behind someone is たくや, and behind たくや is 彰.
Your second sentence gives the opposite ordering:
[彰] は [たくや] の後ろに [座っています]
In this case, 彰 comes first, and is marked with は, indicating that he's the topic - we've been talking about him already. たくや (or I suppose the space behind him) is now the focus - the new information. We know who 彰 is; what we want to know is where he is.
My immediate interpretation of this sentence makes it sound like the answer to a question - 「彰はどこですか？」「たくやの後ろに座っています」. You could strengthen this sense of response by replacing は with なら, making it more like 'if it's 彰 you're looking for, he's behind たくや.' It could also be the 'contrastive' focus mentioned above (this guy is here, and 彰 is behind たくや), or it could be setting a new scene with characters we already know (imagine the first paragraph of a new chapter - '...We're all gathered around to listen. 彰 is behind たくや...').
So as much as these two sentences do describe the same physical reality, the contexts you'd use them in are really quite different.
(*They're probably clitics, not particles, but that doesn't matter here)
(†Technically it's not so much that が marks focus, it's more like leaving a main clause subject unmarked for topic implicitly marks it for focus. There doesn't seem to be a way to just leave a subject unmarked for topic/focus status unless topic and focus are both explicitly assigned to other things.)