SSD is not recognised with the internal SATA cable (13" 2010 MBP) It's pretty weird, seeing that HDD's are recognisable, and that SSD works when in an enclosure (Crucial M500).

I've read somewhere that it could be an issue with the cable, but I bought a replacement cable, and it doesn't recognise the SSD either.

One idea that I have might be the issue is that the SSD needs 1.7 A of current, while the HDD I tested it with only 1 A.
The actual problem here was that I installed the OS while the SSD was in an external enclosure, not installed in the internal bay. When I wiped the drive, installed it in the bay and then installed the OS from the old HDD, now in an external drive, my problems were solved.

I also tried another SATA cable before switching the positions, and that didn't help.