I googled "Sony Vaio W22M1E" and found this [PDF link to a User's Manual.](http://Sony Vaio W22M1E) I don't know if this will have an installation section in it (some computers have one stick of memory on the back, another under the keyboard (ugh).
Opening up the back and seeing if the RAM stick model-numbers match may be the best info for you.
Sadly, that Google Search's first page didn't get me to any useful Sony tech sites, I note.
"More RAM" is indeed one ingredient to a faster computer and, as you suspect, "more Correct RAM" is the right ingredient.
It looks like Sony makes it difficult to find it's tech manuals, so I hope that User Manual comes in handy.
(You might try selling websites - NewEgg sells memory for notebooks, and their website might offer the specs; these would have originated from Sony.)
Also, memory sticks will have a Speed Rating - "333" or "533", "400" or some numeric value. You might see if those match, OR if you can locate your current RAM, post both sticks' model numbers here.
The acid test for memory is unplugging the Old Memory and remove it completely, and then install one stick of the 'new' memory and see if the computer boots up. THEN go back and add Old Memory and see if the computer will recognize both.
If these are mismatched speed, computers tend to slow down the Fast Memory and only use the slower speed for all operations. So, you may be throwing an anchor and dragging it along instead of speeding up the computer.