Right of way comes in three grades: 'Separated', 'Exclusive', 'Dedicated'.
Dedicated is the lowest grade. A lane nominally belongs to one mode, an obligation more commonly honored in the breach. Think of HOV lanes and bicycle lanes.
Exclusive can be though of as 'excluding'; exclusive use is maintained through barriers. Exclusive guideway is never continuous--there are always gaps in it, typically at intersections.
Separated is similar to exclusive, except that it is continuous. Typically, this requires grade separation, if only where the guideway intercepts other rights of way.
Heavy railways (commuter rail, freight rail) have separated guideway, for the simple reason that trains can't stop quickly. Where they must cross other roads 'time-separation' (railroad gates) are used. Where this generates unacceptable levels of delay for the cross-streets (a train can take minutes to pass) grade-separation is used. Typically, this requires an overpass for cars traveling over the road. In cases where there are too many roads, the railroad may be buried. The 'cut and cover' model of a trench with a roof were how the first subways were built. (Actual tunnels came later). In some cases (Alameda Corridor, in LA), digging an uncovered trench for the railway is simpler than many bridges.
Light railways have a mix of Separated, Exclusive, and Dedicated. Most light railways make use of some portion of old freight track, which are already time-separated. Some light rail systems provide Separated guideway by running down the center of freeways (Portland) or on elevated structures (Los Angeles, Salt Lake). Light rail on streets (a train in in tram-mode) typically has Exclusive guide way, with intermittent sections of Dedicated guide way. San Diego and Buffalo, two or the first cities to build light rail, made use of this. Light rail vehicles weigh less than heavy rail vehicles, and so can stop more rapidly. Streetcar/Tram vehicles weight even less, so they can stop faster and are even more suitable for on-street use.
The decision to use either Exclusive or Dedicated right of way is one of cost and safety. Without barrier separation, conflicts with turning cars results in accidents. Sadly, even Exclusive guide way is no guarantee against human stupidity.
Higher barriers, which prevent drivers from crossing them, may be safer. The trade-off is that first responders/emergency vehicles lose the ability to make left-turns and U-turns across the street, due to the curb. To accomodate this, curb heights vary between systems.
There is a fourth grade of right of way: Shared. This is what regular buses have. It offers no speed advantage to the transit vehicle over a regular automobile. Once the time consumed with exiting the flow of traffic, boarding and alighting passengers, and re-entering the flow of traffic is considered, transit vehicles in shared right of way travel at about half the speed of an automobile.
In contexts where right of way is scarce or political will lacking, Shared and Dedicated guide way are more common, to the detriment of transit vehicle speed, reliability and safety. A streetcar operating in shared guide way has minimal advantage over a bus. (The minimal advantage is that is cannot leave the flow of traffic, and so loses less time entering/leaving the traffic lane).
BRT systems are cheap to build, and largely unregulated. Consequently, they vary wildly. They make use of every kind of guide way.
Grade-Separated
Time-Separated
(LA Orange Line), for a time. Drivers ignored them, causing crashes. It still experiences issues with drivers running red lights. Grade-separation is in the works.
Exclusive - Fenced
Exclusive - Curb
Dedicated - Median
Dedicated - Side
