No, they are not the same.
17HMR is a rimfire basically the 22WMR necked down to 17
17 Remington Fireball is a centrefire cartridge, it's a necked down 221 Fireball, it was called the 17Mach IV at one time.
17 Remington is also a centrefire cartridge, which is based on the 222 Remington Magnum casing.
Neat calibers and very addicting. Be careful!