What are these formats, why is my camera choosing different formats while i'm shooting, and what is the easiest way to change them back and avoid in the future?
Every major camera manufacturer has their own proprietary raw image format (and some have more than one). CR2 is one of Canon's, and RAF is one of Fujifilm's. What you have is a memory card that spent some time in a Canon body, and was not cleaned off before you moved it to your new Fujifilm.
There are only two formats your X-T2 can record. One is a JPEG image with the .JPG extension and the other is a RAW file with the .RAF extension. Other extensions, such as .CR2 for Canon, are used by different manufacturers. In no case can your Fujifilm create a .CR2 file. If you have one on the card it was created using another camera, specifically a Canon.
The format is always under your control. You can set it using the menu or the Quick Menu activated by the Q button. Move the the Image Quality option and use the rear control-dial to choose the format you want. RAW means the camera produces a .RAF file, Fine and Normal means the camera stores a .JPG, the difference is that Fine which is less compressed than Normal. There are also RAW F and RAW N options which saves both files with each shot, meaning you get a .RAF RAW file plus either a Normal or a Fine JPEG image.