The specifications of my system say it supports 400 MHz and 533 MHz DDR2 unbuffered SDRAM. I have a 1 GB DDR2 PC2-5300 laptop RAM module. Can I use this in my desktop? If not, what exactly is the difference between desktop RAM and laptop RAM?
In your case, the answer is no, as you have stated your PC uses SDRAM. However, the answer in general is, "It depends." It really depends on the motherboard manufacturer. Typically the answer is no, however there are some "desktop" models that use SODIMMS. Typically these desktops are small form factor and use laptop SODIMMS to save space.
As it seems the question is still getting views and being used to close new questions as duplicates I'll add the current answer.
There exist adapters, both for DDR3 and DDR4 that allow using SO-DIMM modules in a DIMM socket, here is an example from Aliexpress.
They have been tested by multiple people to be working, for example Linus Tech Tips.
There is a difference in pin count between the connectors but the added pins ade not connected, optional or duplicates.