Stand up to or stand up against?

Which of the following expressions is correct: "to stand up to someone/something" or "to stand up against someone/something"?

If both are possible, do they have the same meaning?

If not, when should I use each of them?

Would you please give me some examples?

For instance, do you stand up to a school bully or do you stand up against a school bully? Do you stand up to a company polluting waters or do you stand up against a company polluting waters?

Thank you.