Why did the Macedonian Empire cover an almost identical area to the Achaemenid Empire?

Quite simply because Alexander conquered the Achaemenid Empire. That's why ancient authors saw him as Alexander the Great. He conquered the longstanding, monopolar super power of their known world. There's really not a whole lot more to explaining how and why Alexander's borders lined up with the Achaemenids. He took over the old power after securing control of Greece and his father had conquered most of Thrace. It's actually a lot more complicated to explain the parts of the two empires were different (which again were really just one empire under different management). I've actually answered that question before in this post.

Now, his motivations for embarking on those conquests specifically are more complicated, but I'll also point you to older answers for that information. Namely my own perspective in this answer and u/iphrikates' reasoning in this one. There were logistical reason and ideological reasons that both of us address differently, but both of our answers ultimately deal with the issue that there just wasn't a lot in Europe to draw Alexander's attention.