Do Americans and Brits are speaking the same language?

I don't know why Americans called football as something like rugby while soccer is football as many Europe and Asian countries.
Wait, I list the words..
It gets me mixed up.

Lift=Elevator?
Trousers=Pants?
Holiday=Vacation? They are same meaning. How can you be confused?
Football=Soccer
Bin/Dustbin=Trash can?
Autumn=Fall?
Toilet=Restroom? How can you rest in a toilet? Hmm. 🤔
Aluminium=Aluminum?
Petrol=Gas?

Etc..

Blimey, I need to learn American English.