There are no big difference rather than naming. Use whichever you prefer: href="/manifest.webmanifest" or "/manifest.json". Just don’t forget that MIME type has to be: application/manifest+json in both cases.
<link rel="manifest" href="/manifest.webmanifest">
<link rel="manifest" href="/manifest.json">
Note that spec says it should be manifest.webmanifest. And later it may be important because it is under heavy development.