On Steam, there are the labels "Free" and "Free to Play" - what is the difference between the two?
"Free" means the game is free. 100% free with no charge to play it.
"Free to play" means the base game is free and you can play for free but some content will be available that require micro-transactions or other form of payment to get hold of. As mentioned on the Steam Support article for "Free to play" games:
Free to play games are available to download for free and can be played without a subscription or a credit card. Your Steam wallet allows you to purchase items and content in-game to customize your gameplay.
It's important to note that in most cases, at least on Steam, if a game is listed as "Free to Play" then the additional content which is behind a paywall will be purely cosmetic.
In other words if you want your player character to be wearing a fancy hat or have a weapon which is golden rather than the usual chrome or black finish then you will have to pay for it, but the actual gameplay will usually be unaffected.
Examples of this model are DOTA 2 and Team Fortress 2.
Some other games have items/bonuses etc. which do affect gameplay, which can be unlocked over the course of normal play, but will allow you to unlock these things more quickly by paying some money.
Sometimes you can outright buy these items, or sometimes you will earn free "points" of some type by just playing which can be spent for either cosmetic or gameplay-affecting items, and you can "boost" the rate at which you earn these otherwise free points by paying real money, thus allowing you to unlock the items more quickly (but still requiring you to "earn" the points through some gameplay actions or just time spent playing).
Examples of this model are League of Legends and Marvel Heroes.