Ogg is a lossy formar, Wav is not. They are not compatible.
The question should be "Flac or Wav?" And the answer is Flac, unless you need some kind of old compatibility.
Lossy means that data is lost on encoding, so the original quality of the recording will be compromised in some fashion.
FLAC is superior to WAV because it's still lossless but compressed so the files take up less space.
I thought ogg had multiple formats, some of which weren't lossy.
Depends on what counts as "better".
Better quality? WAV, since it's lossless.
Better efficiency? OGG (well, Vorbis) since it compresses pretty well, but you'll still get a (minor) loss in quality.
That said, both of those formats are old news and should only be used if you have weird, specific compatibility needs. For lossy compression, OGG/Vorbis has been succeeded by Opus; it's what YouTube uses, compresses fantastically, and is supported by damn near everything. For lossless, FLAC (Free Lossless Audio Codec) is still the gold standard: you can reduce file sizes by as much as 60% with literally zero loss in quality. If you can, use one of those.
For what? wav is your lossless container. Pretty much universally recognized. Think of it like RAW for photos. ogg is lossy and more appropriate for most use cases, but is not universally recognized and not available on all devices.