Territories is a game type introduced in Halo 2 and does not appear in Halo: Combat Evolved. It is a battle to control the map by reaching a certain point, taking it over, then you must keep it in your control for a certain amount of time. Most of the time you will need several areas under your control to win. In each map there are four areas to control but this number can be lowerered to one.
This is a team Objective Based Game.
Race is a game type introduced in Halo: Combat Evolved and was taken out of Halo 2. It is possible that Territories originated from Race. The objective for Race is to be the first to get to the holographic flags which are called laps. There are different ways to play Race you can get the flags in order or in Rally you can get them out of order which is a lot like Territories. Accept in Territories you have to wait by the plot for a few seconds. In Race you just have to touch it and move on.
This is both a FFA and Teamed Gametype.