English Grammar: Prefer vs Would Rather

I prefer to eating pizza

I prefer eat pizza

I prefer eating pizza

I prefer to eat eating pizza

I would rather to stay home

I would rather stay home

I would rather staying home

I rather to stay home

I prefer tea than coffee

I prefer tea to coffee

I prefer the tea over the coffee

I prefer to tea coffee

They mean exactly the same thing

Prefer is more formal and general; would rather is for immediate choices

Would rather is more polite

Prefer is only for past situations

Would rather to going

Would rather going

Would rather go

Would rather goes

to walking

walk

walking

to walk to

I would prefer going

I would prefer to go

I would prefer go

I would prefer goes

I prefer reading than watching TV

I prefer to reading to watching TV

I prefer reading to watching TV

I prefer read to watch TV

I would rather you come yesterday

I would rather you came yesterday

I would rather you to come yesterday

I would rather you coming yesterday

Would rather

Prefer

Both interchangeably

Neither

I would rather to not go

I would rather don't go

I would rather not go

I would not rather go

I would prefer going

I would prefer to go

I would prefer go

I would prefer gone

Prefer

Would rather

Both equally

Neither

I prefer having gone to having stayed

I prefer went to stayed

I prefer to have gone to have stayed

I prefer going to staying

I would rather you to go

I would rather you going

I would rather you go

I would rather that you going