Wi-Fi is doing no extra compression to get the sound to you.
Bluetooth, while it's come a long way, uses extra compression because of the limited bandwidth/data transmission. The majority of bluetooth devices are capping audio at 256 kbps. Even AptX HD, which advertises that it can play 24-bit/48kHz files, is only giving them to you at 576 kbps. Then typically, there's even more audio magic on top of that inside your speaker or headphones to help "recover" that audio data.
There's a lot more detail but it's important to keep it understandable.