The two speaker types differ based on the characteristic of the sound.
Cinema speakers is the term used for limited bandwidth speakers. Their power requirement is less. They are supposed to sound crisp and exciting. The sense of power generally comes from the subwoofer.
Speakers for music are supopsed to be full-range. They need and can handle much more power. They also can be termed as warm, bright, tight, hologenic etc, depending on their sound characteristics.
The "labeling" you are talking about are purely indicative. Both can be used in both types of applications. How they will sound depends on more on the source and the amplification than the label they carry.