When it comes to FM or TV reception, there are two relevant mantras:
- Location, location, location
and
- It depends
FM radio frequencies behave essentially as line-of-sight transmission, however they do bend a bit over the horizon, especially with overcast cloud cover at the right altitudes. FM radio frequencies also can reflect off of tall buildings or hills.
The higher the antenna, the better it works.
The farther you are from a station, the more you need a high gain antenna and a rotor. However, in urban locations, reflections from tall buildings can also make a rotor necessary. So, it all depends on your location and the location of the broadcast stations of interest.
Expect to receive FM broadcasts from stations no more than ~25 miles away with an antenna with modest gain, such as the standard folded dipole that Yamaha probably supplies. Higher gain and a narrower 'field of view' come with Yagi-Uda or log-periodic type antennae. They can receive stations from ~50 miles away, and under the most favorable circumstances, as far as ~80 miles. The Radio Shack antenna you mentioned is probably one of these types.
I live on a hill about 15-20 miles away from most FM stations in the Washington area, and about 40-50 miles from those in Baltimore. I use an omnidirectional turnstile type dipole antenna in my attic. A high gain antenna, one with narrow field of view and a rotor, or a tall rooftop mast aren't needed in my location. In that sense, I'm lucky. Your luck depends entirely on your location.
A good general discussion can be read here:
https://en.wikipedia.org/wiki/Antenna_(radio)