What are the differences between a U.S. territory and a U.S. state?

The Constitutional basics are:

1) only states have voting representatives in the House and Senate;

2) Except for D.C., only states have electoral college votes (although both major parties allow territories to participate in the nomination process);

3) Territories are subject to Congressional control (meaning Congress can change the borders at will and make laws that apply to specific territories).

Because of the third, there are a lot of specific laws that apply to specific territories.  For example, under current law, territories can't declare bankruptcy (states can).  For this reason, Puerto Rico is subject to a federally-established board related to its debt issues.  The best way to think of it is that a territory at the national level is similar to a city at the state level.

The simplest way to put it, is that territories  are like incorporated parts of the United States.....that do not (yet)  have FULL US statehood. 

They are under the jurisdiction of the US  and therefore have SOME US rights,  but NOT all.  They are not sovereign nations, but neither are they  equal with STATEHOOD- 

There has been much talk of making Puerto Rico a state,  while some territories actually dream of Sovereign status....and going their own way, 

One's a territory and one's a state.