All the options for fetch in Google search console has a different purposes
Desktop - This is default and this option is for the website which can crawl images, videos, webpages and all that.
Mobile smartphone - This option is for Google smartphone crawlers.
Mobile xHTML - This option does not support rendering and Uses the SAMSUNG XHTML/WML crawler.
Mobile cHTML - This option is mostly for the Japanese feature phones which Uses the DoCoMo Google Mobile crawler and this option also does not support rendering.
Source here
