They tend to work in a capacity similar to a US State, e.g. Utah itself but there is a lot of variation and nuance from tribe to tribe and state to state. You

They tend to work in a capacity similar to a US State, e.g. Utah itself but there is a lot of variation and nuance from tribe to tribe and state to state. You will run into confusing situations where a county law enforcement official might patrol on a reservation because there is overlap or nebulous boundaries with the blessing (cross deputizarion) from the tribal law enforcement. However some tribes defer more of their governance to a Federal Bureau of Indian Affairs. For a largely autonomous example, the Cherokee in North Carolina are interesting. Largely funded by their casinos and now marijuana which is legal on their reservation but not the encompassing state of North Carolina. They have fairly strict rules around membership, such that a Cherokee that was shipped off to Oklahoma is not eligible for membership. Land ownership is based on tribal membership, not quite following standard American rules. It’s a fun deep dive to read up on their system.