Mike Hurst has the correct answer.
The names of the two technology's are descriptive as to what they do.
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A booster is just that. it BOOSTS the signal. A repeater, on the other hand, receives the signal, then repeats it on a different channel.
Most of the time, a booster is a better antenna or antennas. This "passive" approach is best for boosters as the better antenna will increase the gain of both the transmitter and receiver equally. Generally, one would replace the cheesy antenna on the router as putting it on a laptop will impact portability.
To get more distance, you might put a better antenna setup on both the router, and the desktop several hundred feet away. If you really want to get boost (pardon the pun,) look into directional antennas. they will focus the radiated power in a single direction. You may be able to get 5000' or more with 2 high gain directional antennas. But, of course, portability wouldn't exist.
Antenna design is EXTREMELY complex. There are many factors that go into making an antenna. When you start getting into antennas with multiple elements, they will interfere with each other and a poorly designed antenna may not work nearly as well as you might hope. Read reviews on any specific antenna setup you are thinking about getting.
Sometime a booster is an amplifier in the signal path (wire) between the antenna and the network radio (WiFi router or WiFi card.) This is called an "Active" booster. The amplifier will increase the transmit power a lot, but the sensitivity of the amplifier may not do a good job of receiving signals so you may not realize the best distance. Think of 2 people, Mr. Router with a bullhorn and Mrs. Desktop without. Mr. Router can "talk" (yell really) and Mrs. Desktop can hear, but Mr. Router cannot hear the low level from Mrs. Desktop.
If you can get 2 active boosters (one at the router, and the other at the desktop/laptop) then poor receiving is less of a factor as both are yelling louder.
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A repeater, on the other hand, is just that. It receives the radio signal from one point (lets say your router) then retransmits it on another channel to another point (say your laptop). This will increase the latency (delay) as it has to receive a packet, store it, then retransmit it. These packets are fairly small, and they go by pretty fast, so I would guess there would be little impact in observable speed degradation, but the extra radio will add several problems to the "system".
You could even combine repeaters and passive or active boosters, but when you start getting into this realm, you are on your own.
Good luck.
Mark.