The stipulation for Caregiver amount is that the Dependant must live with you.
For Infirm Adult Dependent credit , a requirement is that the dependant is a resident of Canada. There is no requirement that the dependant live at another address from you, though they might.
Other than those stipulations, either credit could be claimed, but only by one person for the same dependant.
Caregiver credit does have rather wider application, for example for parents over 65 but not considered infirm. However there is an area of duplication in the credits, which awaits a cleansing of the schedule 1 credits.
