The concept of casino money is slightly different for online and land-based casinos. At the land-based house everything that you buy at the cashier window is the money of that casino, and can include chips, coins for playing slots, and plaques (which are bigger in value and size than the chips, but kind of the same). Other than winning more of them during the game, you cannot get them for free. There are some exceptions: certain regular members can get some free chips to play, but it happens on a rare occasion and usually in small amounts.
Online, there are two concepts behind it. One is similar to the mentioned above. You log on to a gambling site, transfer some funds from your bank account and purchase a certain amount of chips. You bet them, you can lose and win them, basically the same as a normal casino, and it is all presented in something like the point system. However, online you can also play for free and receive no deposit casino money. Mainly such money can be used to play free games, where you cannot win anything, but some casinos offer a small amount of casino cash for you to use and try to win some real funds.