We recognize the 45 for its 7″ diameter and large spindle hole. It’s obvious why it’s called a 45 – it spins at 45 RPMs. It’s other name, “a single” is pretty obvious too. There’s a single song on each side.
The 78 is similarily named for its speed of rotation.
An LP or “long play” or “long playing” record makes sense too. Both 78’s and 45’s held one song on each side (about five minutes maximum for a 78), so the 33 1/3 with its slower rotation and thinner groove played longer.
But why “album” for a 33 1/3 LP?
When the 78 was the only record available, only 5 minutes of recorded music could be recorded on each side of a disc. Most of the recordings were classical and much longer than 5 minutes necessitating the use of multiple discs for a single symphony. These discs were put in paper protective sleeves which were bound into books that resembled photo albums – hence the album stuck as the name for even a single LP because it held more than a single song on each side.