voltage and current amplifier

voltage amplifier does voltage amplification
current amplifier does current amplification

Is there something like power amplifier or power amplifier is just same as current amplifier?

Technically, all amplifiers are power amplifiers - because where there is voltage there will be current and vice-versa, and therefore power.

However, what differentiates a voltage amplifier from a current amplifier is that a voltage amplifier typically does not have any significant current sourcing capability - its output requires a high impedance load, but it can provide a large voltage gain. A current amplifier, on the other hand does not have any voltage gain (its o/p voltage is equal to its input voltage) but a much lower impedance load can be connected to its output (i.e. it can provide a large current gain).

Voltage amplifier has very high input impedance, high voltage gain and low output current.
Current amplifier has medium to high input impedance, low (unity) voltage gain but large current gain (large output current).

A power amplifier = voltage amplifier + current amplifier.

ASSUME:if suppose a speaker having low impedance ,then power amplifier want to amplifies the current to drive the speaker
ASSUME:if suppose a speaker having high impedance ,then power amplifier want to amplifies the voltage to drive the speaker
am i right?

If you are talking audio amplifiers, then there are proponents for current drive, although the majority of speakers are voltage driven. Note in either case, they are power amplifiers, that is they have power gain from input to output, and that the speakers are both low impedance, say eight Ohms.
See link below for a current drive proponent. The voltage/current argument for driving speakers is an on going one, and often starts fierce debates.
http://www.current-drive.info/6
Cheers,
Richard