For the OP: The stock hole is 1/4" NPT. Your aftermarket gauge is likely 1/8" NPT. So get a brass tee from the hardware store, along with the appropriate adapters, and plumb both senders into the Tee.
Your observation is correct - gauges are sender specific. No mixing and matching; no using one sender for two gauges.
For water temp, personally I would put the new gauge's sender in the stock (most accurate) location. Then remove the brass plug in the rear of the lower intake (driver side) and put the stocker there. Or get a tapped waterneck from the parts house (10 bucks) and put the stocker there. This latter location is inaccurate if the t-stat sticks but you're probably not going to look at the stock temp gauge much anyhow (the real point is to not have a dead gauge).
Dont try to use a Tee housing two temperature senders (in case this sounds like an easy way to do things).
Good luck.