agree with rolli59. Although from same manufacturer and on the outside they seem similar, they can have different memory chips, eg Samsung, Hynix etc and density. This is where the issues arise. If they are not matched DIMMS as rolli59 has said, they can have problems working together.
With that said, if you get the second stick, you will most likely be playing around with the timings to get both to work together.
I'd advise buying a kit, and then trying to sell the old stick to offset the cost.