So we're comparing the European rabbit with the pet "version". They are actually the same species. The European rabbit is Oryctolagus cuniculus, whereas the pet are Oryctolagus cuniculus domesticus. In general, this means that they are pretty similar (mostly), especially in bodysize.
Similarly to dogs, a lot of different breeds of domesticated rabbits exist. Because rabbits serve no real "functional" purpose, these variations are less extreme than the functional differentiation in dog breeds, but still. Take a look at this list of rabbit breeds to find the extent of breeds.
The European rabbit is generally brown, for optimal camouflage in grassy and sandy areas. This is boring of course. As a consequence you'll see that many of the different breeds differentiate in colouring. As a result, the colouring is a decent discriminator between wild and domesticated rabbits.
Plenty of domesticated breeds have floppy ears. This is something that you're much less likely to see in wild rabbits.
One specific breed jumps to mind (pun intended) that does have brown fur and standing ears, which is the Flemish giant. These get significantly bigger than normal though. Whereas wild rabbits grow to about 40 cms in size and 2kgs, big Flemish giants can grow up to about ten times that weight, sizing over 1m. Take for example this photo taken from the Wikipedia page (link above):
Another perhaps obvious distinction is their behaviour around humans. Rabbits are very flighty. Their only defense is being able to outrun threats towards their nests, beating them there and hiding undergrounds. Wild rabbits will generally use this when approached. Domesticated rabbits are less likely to run away. Of course this should go with a grain of salt, as domesticated rabbits that ended up in the wild might show this same behaviour, but I did want to mention this.
Even wild rabbits living in contact with humans will be flighty. Maybe even especially, I don't know. There were rabbits around my university, making their nests under the buildings only a couple of meters away from the lunch areas outdoors. Even though they came in daily contact with humans that did them no harm, they still wouldn't allow anyone to approach them without making a run for it.