A Hierarchy of Interactive Systems
As I said, a lot of different types of media get bunched up together in a giant bracket we refer to as "video games," but as I also said, I think we all know that games are also their own unique thing when it comes to any non-digital fields. Employees at Toys R Us have no problem separating their puzzles from their board games, each of which usually get their own separate areas, for instance.
I've created a chart that illustrates the relationships between some of the different types of interactive systems that we encounter in the world casually known as "games":
This image illustrates a proposed hierarchy of interactive systems.
Simulators (Examples: Flight Simulator, Sim City, Dwarf Fortress) -- A simulator is a type of interactive system whose primary responsibility it is to simulate something.
In the end, one of the interesting differences between a simulator and a game is that it's not a valid complaint to say that a simulator isn't fun. Simulators really have no inherent requirement to be fun -- they only need to simulate something.
So, you could have a simulator that simulates something fun and interesting as in Dwarf Fortress, or you could have a plant-growing simulator. It's worth noting that even in Dwarf Fortress, there's no guarantee that anything particularly interesting will happen.
I recall one game where my fortress went totally undisturbed, with almost no significant events happening for many hours. Were it a game, I might be disappointed, but given that it's a simulator, I actually appreciate that this is a real possibility.
To be more precise, the real difference between a simulator and a game is that a simulator is not a type of contest, and a game is. Of course, I suppose you could have a "contest simulator", but the fact remains that competition is not an inherent part of simulation.
Contests (Examples: a weightlifting contest, Guitar Hero, Simon) -- All games are contests, but not all contests are games. The issue is that while contests are competitive, they do not require meaningful decisions. They are often a pure measurement of ability -- a simple question of "how much weight can you lift", or for the example of Guitar Hero or Simon, "how well have you memorized this sequence". It can be a bit hazy in some situations, but generally I think most of us have a pretty good innate sense of what the difference is between a game and a contest.
One exception to this would be something like Guitar Hero, which I expect that many people would be appalled at the thought that it is a contest, and not a game. Firstly, you should know that calling something "not a game" is not a value judgment, although it's often mistaken for one. I personally believe that Guitar Hero is a lot more like a contest than a game, because it is a pure measurement of ability, and I would argue that little or no meaningful decisions can be made during play.
Puzzles (Examples: a Portal level, a jigsaw puzzle, a math problem) -- A puzzle is another word for "a problem". A puzzle has a single correct answer -- a "solution".
Some games can also be solved ("perfect information" games, such as chess, where all the information about the game state is known to the player), however if it is common for people to be able to solve a game, it's considered a knock against that game (Tic-Tac-Toe is solved easily by most people other than very young children, and therefore it is not considered a good game for adults). Puzzles, on the other hand, do not get a knock for having a solution; that's what they're all about.
So do puzzles have "decision-making"? I argue that they do not -- at least, certainly not at all in the same way that games do. Puzzles are not games, because while some puzzles allow players to make decisions, this is actually rather irrelevant to the outcome. All that matters for a puzzle is whether or not the player gave the correct answer.
If a math problem asks four plus six, if you say 10, you have solved that puzzle. What you did along the way changes nothing about the outcome. So, while you can make decisions while attempting to find the solution, these decisions are actually irrelevant to the puzzle. In games, decisions that are made by the player have effects that change the state of the game, and the outcome of the game. So in games, a player's decisions really matter in a way that they don't in puzzles, and this is the way that I draw the line between games and puzzles.