How are laws different when in a Native American reservation (that matter to a tourist)

Reservations are semi-autonomous lands. They have their own rules, law enforcement officiers and judicial systems. But that said, their laws are not really that different than the state they reside in.

They are often more strict on enforcement, so obey the speed limits and other driving rules, don't count on the 10 miles over the limit grace a state trooper might allow. And definitely don't drink and drive, alcohol is a big problem on many reservations and the reservation police / judges are quite strict on that.

One aspect though that Google maps don't address adequately is designating private roads. If a road has a national, state or county number then they are public access. But if your proposed road has no number, it is best to ask locally before proceeding, to avoid trespassing.

Presuming you are a non-Indian (not a member of that reservation, nor a different tribe) they only have limited jurisdiction over you. Most Indian reservation police have cross-agreements with the state cops to allow outside cops (such as pulling over a car on the interstate traveling through reservation lands) to operate normally, or to hold you till the Indian cops get there. So don't think by crossing the border/sign or leaving the border/sign of Indian lands, that you're going to get away with anything.

Also keep in mind, that even when you're in an Indian reservation, you're still in whatever US state you are in.

In terms of major crimes, if it's two non-Indians then the tribal courts have no jurisdiction (generally it's state or federal jurisdiction). If it's two Indians (even both from another tribe) then local tribal courts have jurisdiction. If it's mixed, I believe tribal courts have jurisdiction generally. If the major crime is also one of a specified number of crimes, federal government can also have jurisdiction.

In short, "it's complicated" (as a previous poster said), but as a non-Indian you don't want to find yourself in tribal court, especially for committing something more than a minor infraction.

There can be and are some legal differences between laws and traffic regulations in reservations and out of them. Example from Montana. Those are however minor. In the US there are also variations between states, but all the time masses of tourists cross state lines without knowing the ins and outs of the traffic laws applying to all the states they are crossing. The same holds for the reservations. Just drive carefully and if you doubt if something is legal, just don't do it.

One particularity that I know of, not traffic related and not relevant for you, but relevant for tourists that go there, is in the Arizonan part of Navajo Nation. Navajo Nation adheres to daylight saving time (DST), while Arizona doesn't. This implies that half of the year the time in Navajo Nation is different from the rest of the state. Source Navajo Nation also covers part of Utah and New Mexico, but those two states do observe DST, just like Navajo Nation, so there the time is the same as in the rest of the state.