Sprite is just a term for any kind of particle like polygon that faces the camera like a billboard. The default particle emitter in cascade will emit sprites. You can make them non-sprites by turning off camera facing or making them into mesh emitters instead.
Flipbook is a term specifically for a texture that contains many sub-frames of an animation sequence. Many explosions and water splashes have a flipbook at their core. Also, often times FX artists will use a flipbook like texture but really just pack different variants of smoke or something in each frame so at that point it is a tad ambiguous if its really a flipbook since its not truly an animation but just a bunch of frames to pick between. I think it is since you still pay the same cost and it behaves the same.
So many sprites use flipbooks inside of them (called SubUV module by cascade btw, same thing though), but also many just use panning textures combining with static masks to create the illusion of motion.