Can someone explain to me the difference between a co-owner, a co-signer and a guarantor, and what the requirements for these categories are in regards to joint intent on loan?

I thought that intent to apply jointly for credit applied soley to applicants and co-applicants, but could be wrong.

An "Applicant" is any person who requests or who has received an extension of credit and includes any person who is OR will become contractually liable for the loan. No matter what the lender calls this person (borrower, co-borrower, co-signer, guarantor); if they are or will become liable they are covered by Reg. B thus joint intent.... Keep in mind, that just because someone is a co-owner, does not necessary mean that the person is agreeing to be contractually liable (they may be just signing the security instrument)

See also Reg B sections: 202.2(e) and 202.2(x)