Usage of "Free-to-play"
Solution 1:
I'm not sure there is a formal meaning for the term "free-to-play," but we can talk about a prima facie meaning and a cultural meaning.
The prima facie meaning is as you said: the plain meaning of the words suggests one is referring to any game that one can play without paying money.
Culturally, however, "free-to-play" generally emphasizes the "play" part, meaning you can play it for free, but other aspects of the game are not free. Indeed, the game may be only minimally playable without in-game purchases. Culturally, then, the phrase is meant to emphasize that some, or many, aspects of gameplay are not free, but the game can be launched and some minimal level of playing is possible without paying.
As you observe, "freeware" is a term generally reserved for games that do not charge anything either to run or to enjoy the full game experience. Like other terms such as "adware" (games that require you to view ads to play) or "spyware" (software that installs phone-home programs as a condition of using it), "free-to-play" denotes a kind of game that is partially but not fully free.
Solution 2:
This article explains it better than anybody here can, and it's on the first page for googling "free to play": http://en.wikipedia.org/wiki/Free-to-play
But the gist is this: you're right, free-to-play can indeed mean anything from "completely free" to "free but with paid features". However, lately when people say free-to-play, what they're really talking about is a freemium game.
Solution 3:
Instead of thinking of free-to-play as a specific term (i.e. "this game is free-to-play"), you should think of it as a general, blanket statement for any game that costs nothing to begin playing. All free-to-play means is that you do not pay to install the game/you do not pay to play the game. For example, you're not paying to play Bejeweled Blitz on Facebook. It's free to play.
But, that's really broad, so you could say under the blanket of Free-To-Play games is...
- abandonware: software abandoned by developers
- adware: software supported by ads
- freeware: software with no payments of real money at any point in the game
- spyware: software that installs additional software to be used
- freemium: software with premium content that must be paid for
But some of those things are redundant. For example, is a freeware game free to play? Obviously, right? So you could just call it freeware. I'd say abandonware is in the same boat, but that's up to interpretation, I guess.
But just because something is free to play doesn't mean it's free-to-win, in the sense that you can play it, but that doesn't mean the game is set-up in such a way that you'd win it. Freemium is the biggest offender here, because freemium games are games that hamper completion by making premium content either necessary or the most logical solution to beating the game.
In other words, free-to-play games only imply that playing the game is free. It doesn't say that you can't be interrupted by ads, it doesn't say you can't have microtransactions, and it doesn't say that you won't accidentally install malicious or otherwise software. You can branch out from the general term once you know what the game actually is. (For example, "I thought MLP:Friendship is Magic was free-to-play. Turns out it's freemium.")