I'd sooner starve than eat that disgusting food.
I'd rather starve than eat that disgusting food.
Why 'sooner' becomes 'rather'? Literally speaking, it's weird.
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They are two very different words, but in this context, they both amount to the same thing.
I'd sooner starve - I am going to starve before I eat disgusting food.
I'd rather starve - I would prefer starvation to eating disgusting food.
Sooner here means the speaker would do thing before doing other thing.
Rather is a direct comparison: in the choice of two options, I would do thing and not other thing
I'd sooner . . . is more old-fashioned. I'd rather . . . is used more often now.