I have a 3 years old ThinkCentre (A52, type 8381). It has 1GB of RAM in 4 256MB sticks. According to the model spec, it supports 400Mhz DDR2 memory. I would like to increase the amount of RAM I have, given how cheap 1-2GB sticks are today. However, someone told me faster memory sticks (say 800Mhz) cannot be used when only 400Mhz are supported. This is a bummer, because for some reason 1GB of 400Mhz DDR2 costs about 3-4 times more than a modern DDR2 stick with the same size. Is this really the case? Can't a memory stick work in a frequency lower than its optimal?
The best way to check for compatible memory options is with Crucial's tool -- CrucialScan.exe
It has helped me on multiple old machines (workstations and laptops).
For DDR2 PC2-xxxx and the MHz figures look at this DDR2 wikipedia page.
The two things are similar ways to measure almost the same thing.
Further on your comments, people quote frequencies differently at times (probably to make life more confusing for the buyer).
Not reliably. Dynamic memory relies on being refreshed, and if you run it on a slower frequency than it should, it may not get refreshed quickly enough. You'll run the risk of getting memory errors, which will mean your computer will crash/freeze. (And these tend to get more common as the computer heats up to).
I have had one case of buying the fastest memory that motherboard can support, but then by mistake running it on the default memory speed, which was half the specified speed. The machine would typically freeze on me ever second day or so, and this went away when I fixed the memory speed.
So it might work for you. But don't rely on it. I would go for the correct memory.
The specs on the system you provided shows that you CAN put in PC2 6400 (or 800MHz) RAM. The front-side bus on it supports 800MHz. Therefore, you are able to install the newer type of RAM.
Just because Lenovo cheaped out on the initial build, doesn't mean that the board itself doesn't support the faster RAM speeds.
Go and install away!