I previously discussed how Classic Battletech (CBT) shares basic characteristics with other point scoring games. I think I need to be a little more careful with this definition. In CBT the objective is to accumulate points of damage on the opposing player up to the maximum (damage) that player can take (destruction), at which point a "win" is achieved. There is a fixed goal of reaching some point total, and reaching that objective before your opponent does. There are many games with this sort of fixed goal structure: Hearts, Cribbage, and Star Fleet Battles, for starters.
The distinction I want to make is between scoring points towards some fixed goal, and trying to score more points than the other player with the win going to the player with the highest score at the end of play. Some examples of this might be Scrabble which is limited by the number of tiles, or any game where the score is kept until a time limit is reached. Many competitive sports are of this type, though we don't typically thing of those in the same class as the tabletop games. Some classic two player video games probably also fit into this category: Pong, Tank!, or anything else where you compete for points/scores simultaneously with another player and some amount of skill is involved.
Now I can make some definitions. All the games mentioned above involve some sort of point scoring, but the first paragraph describes games with a fixed objective to win, and in the second paragraph there is no predefined point limit. I will refer to the first type as "Point Objective" games, and the second as "Point Scoring" games. I'm sure there are some other details to be considered, so these definitions should improve with time.
There are still other games where players compete to remove ALL the other players' pieces from the board. (I'm going to exclude games like Chess and Checkers for the moment: Chess doesn't consider the any piece other than the King for a win, and neither Chess nor Checkers have any element of randomization in how the game plays out.) Many games - not just typical wargames - fit into this category: Ogre, Hammer's Slammers, Warhammer (including 40K), and most typical wargames. Collectible trading games games such as Pokemon and Magic the Gathering could also be consider part of the group. However, these games should also be considered in the same class as Point Objective games: Here the points are represented by the individual pieces on the board or map (or starting strength of the player in the collectible card games). Each player starts with a limited supply, and loses when they run out of pieces. This is "Point Attrition" instead of "Point Objective", but it makes no difference if we count points from zero up to a fixed goal, or start at some number and count down to zero.
So now I have definitions. Maybe I need my own Wiki?
Thinking about the dynamics of Collectible Card Games (CCGs), these games don't exactly have a fixed objective, or at least the path to the objective depends on the cards in play, and so may need their own category. I haven't actually played any of these games since my son out-grew Pokemon and so haven't given them much thought. There are aspects of playing for both offense and defense I have not considered.