Flat panel almost all the time refers to your shaker style doors; the extremely plain, basic doors with no 3D design or details. The second image attached is actually an example of a shaker style kitchen. Flat panel or shaker styles are very popular because of how simple they are! You can honestly do a lot with a simple cabinet and can focus/bring attention to other things. Also a good thing to keep in mind is that flat panel can also be called slab doors because both terms are used interchangeably.
Raised panel doors are the exact opposite of flat panel. These door styles are simply raised in the middle hence the name. The look adds depth and highlights the doors. Unlike flat, raised panels have many options as far as door styles go, so you just have to look and pick what you like. Typically you see raised panel doors on a lot of traditional (kitchen) styles because raised panel is a traditional door style. Though just because the style itself is traditional doesn't mean that you have to create a traditional kitchen. There's been plenty of other kitchen styles that have raised panel doors aside from traditional. Once again, it all comes down to what you want in your kitchen.
In regards to both of these panel styles, there's really no right or wrong way as to color/stain or wood type since it all works out well. However there is a difference when it comes to price. Flat panels or your shaker style tends to be less expensive than raised panel. The obvious reason is because there's less going on with that style meaning less detail meaning less work and overall less money it'll cost to build and create compared to raised panels. Overall both panels are sustainable and excellent choices for your kitchen.
In the end it all comes down to what you want and your preferences.
Til Next Time,