That is a better antenna. Not an amplifier.
It is an antenna to have outside in a higher signal area to pick up the signal from the tower. This signal will be greatly reduced inside as the building material absorbs or blocks the radio signals. So the simple idea is to pick up a stronger signal ans fed it via the cable inside the house and re radiate it to make the inside signal stronger. It is not amplifying the signal as such, but bringing it inside by cable and not having it lost in the walls.
A bit like having a light shining through a fiber optic pipe into a dark room.

 

Older cell phones actually had antenna jacks on them. I owned at least one, maybe two of them.

With a booster, there is this thing of frequency response and having to operate in both directions.

With a TV Antenna amplifier which operates below cellular frequencies only has to go one-way.
This on might go to about 1 gHz max.

Audio amps may amplify from about 0.5 Hz to 20 Khz, if that.

Cable amplifiers with broadband services such as Internet have to go both ways, or at least has to pass a signal in the other direction.

Antenna's do have gain, a radiation/reception pattern and they also have polarization or they can receive a better signal based on transmitter receiver antenna orientation.

 

What is the difference between Audio amplifier and RF amplifier

Sometimes the circuit design isn't *ALL THAT* different, but active devices have a cut off frequency that needs to accommodate the frequency you want to amplify. The really big difference is in PCB design and layout - you're not far from the frequency you need to squirt down a pipe (waveguide).

 

Your question is a little bit like saying you want to use a lawnmower engine for a freight train engine. They are both engines after all, so why can't you?
Although it is not a difference in size. The comparison falls down a bit there