Be nice if there was a industry standard naming convention but it appears the more confusing they make it the more junk they get away with selling.
Almost all devices called repeaters receive the signal and then retransmit it. The key issue here is the device must be able to receive the signal in the first place to repeat it. You generally put them at a location in the middle where they get good signal and they can send the signal to a location that gets low signal. This is why these are also called extenders...just depends how you look at it.
True amplifiers are illegal. You can legally increase the signal you receive but you cannot transmit at more power than the legal maximum. Unlike a TV program where you only receive for wireless you MUST transmit. So you could with a amplifier make it so you could receive the signal from the far end but then the far end would not be able to hear your reply. In general amplifiers do not work good even for reception because they also amplify the interference.
The only solution you have is to use direction antenna to attempt to "amplify" the signal in both direction. This is a form of passive amplifier and if you get carried away with the antenna size you can violate the laws. Like electronic amplifiers they only work to a point because you are increasing noise along with signal.
You might be able to use a repeater that has the ability to replace the antenna with direction devices. It really depends how weak the signal really is.