In Formula 1 (but also in all of motorsport) different tyre colours represent different rubber compounds.
The green (wet) tyres are for rain/water on most of the track. The white (hard) tyres generally resist more laps but have lower performance compared to softs
Having the right tyres is extremely important in races where endurance is the focus (that all of F1 is)
The mugs are merging the tyres and the jokes.
To be fair I am stuck on these on my knowledge
And yeah, they never use past intermediate, at least never seen them. So they pretty much are the wet tyres.