PC3-12800S is SO-DIMM memory, commonly used in laptop computers.
PC3-12800 refers to DDR3-1600 memory that has a module classification of PC3-12800.
There are three ways to specify the speed of a memory module:
1) the actual speed in ns (nanoseconds) of the chips on the module (60ns),
2) the clock speed of the data bus (PC800 is 800MHz),
3) the throughput (in Mbps) of the memory (for example, PC3-12800 is 12,800Mbps or 12.8Gbps)
The number “2” or “3” after “DDR” or “PC” is used to indicate whether or not the module is a DDR2 or DDR3 memory.
Sorry, but I wouldn't know what kind of machine you have based on the details you provided.