Difference between server-grade RAM and desktop-grade RAM?

Quality (i.e. reliability), error correction and often the ability to have them replaced when they start warning of failure rather than after failing.

Server ram can be error correcting (ECC) or non-ECC. With the current quality of RAM, ECC is losing ground. The other difference is Registered/buffered RAM. This allows servers to access more ram due to the lower electrical load on the memory controller. Many servers require registered memory but some of the newer servers don't, but even the newer ones can handle more RAM if registered memory is used. Both ECC and registered memory are more expensive than desktop memory.

Hardware is cheap; downtime is expensive.