What types of rail transit modes are there?

Question

For example, like light rail.

Answer 1

1st, there is a general division of freight or passenger rail.  

for passenger rail, subcategories are intercity (amtrak or via rail) or commuter.

for commuter, subcategories are:  heavy rail commuter (examples are metra chicago, metrolink los angeles, septa philadelphia, etc), interurbans (south shore rail indiana), heavy rail transit (like subways/els), light rail transit (can operate in streets and in its own right-of-way - examples include houston, san diego, calgary), or streetcar/tram/trolley (operates mostly in streets only (examples - memphis, new orleans).

there is a new type that is coming, the DMU.  prototypes are built and touring the country, but none in actual operation yet.  they are combining the strength and operational standards of heavy rail, but being used as a single self-propelled vehicle like transit, without a separate locomotive.

each of the above sound somewhat similar, but there are characteristics, such as right-of-way or weight/materials of the rail cars) that is the differentiating factors.  

im not quite sure if this is answering your question, but i hope so, since you simply asked for a list of types.  

if you have a more specific question or need more information about some type or some city, please update your question, ill try to help you more.