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Bumping this to see if anyone can answer.
Do you mean "different" in ways (edit: not) necessitated by hardware constraints (eg. an entirely different look)? If not, it doesn't strike me as tropeworthy, just something that happens because computers and phones are different.
Edited by Synchronicity
More specifically, complete redesigns of a website.
I don't know that we have a lot of tropes specific to page layout
, do we? If we do, never mind the rest of this, but the closest things I know we do have are probably more related to porting games, Updated Re Release, Multi-Platform, Reformulated Game, things like that, which might include changes to the UI or interface.
Might be a good thing if we had some people familiar with formal graphic design to take a look at drafting some TLPs.
Dunno if it'd be a trope, but it could be Trivia.
Currently Working On: Incorruptible Pure Pureness
True, it would depend on the extent to which it contributes to the fiction/interactivity of the site, assuming the site has either.
A website looks different between desktop and mobile.