Yeah, the word "active" can be misleading.
Like Rich says, "Active" refers to the crossover or "system. An "active" speaker does not need to have an amp inside it. For example, the Linkwitz Orion is an active speaker, but both the crossover and amps are external (each speaker requires 4 external amps).
A "powered" loudspeaker does in fact have at least one internal amp. But NOT all "powered" speakers are 100% active.
For example, some "powered" speakers have one amp just for the active woofer, but the midrange and tweeter are passive.
Confusing as hell, isn't it?