Chromium is an open source project launched by Google and Chrome draws its source code from that. There are a few differences between the two browsers. Chrome adds a bit more to the source code and those additions are not open source (i.e., free to distribute with no restrictions). Chromium, for example, doesn't have as many built-in functions but those can be obtained through add-ins. Chromium also natively recognizes fewer audio and video files (but that functionality can be added in).
In short, there's not a whole lot of difference and most people won't notice because the two browsers are very similar (the main difference, honestly, is that Chrome has a colorful logo while the one for Chromium is blue). A lot of Linux distros come bundled with Chromium, so you are likely using that if you have Linux.
In other words, Chrome is based on Chromium but they two are almost identical except for a few proprietary differences in Chrome. Yes, it's a confusing world.