"Your best bet would be to buy the same identical 2x4gb kit you have and use that for a total of 16gb. That will most likely work fine. " Vendors sometimes change chips on their modules and the new chips may have higher densities so they may not work together.
Absolute best bet would be 2X8GB and sell your old DRAM.
They sometimes do, although its not often that it changes especially within the same exact model number. That was more of a thing many years ago, but nowadays there are only 3 vendors of memory chips Hynix, Samsung, and Micron. Not only that all 3 use the same machines to fab their chips (I used to work for the company that makes the machines), so tolerances are much closer.
You're correct, the 100% safe bet is replace all the ram, but these days the chances of ram, especially the exact model from the same vendor, working together, is higher than ever. Clearly the OP is budget limited if hes asking about trying to use 1 additional stick of ram, this route is more than a safe enough risk.