The difference is in the height and capacity. The 2016 is 1.6mm (hence the 16), and the 2032 is 3.2mm (again, 32). The capacity on the 2016 is only 80mAh, and the 2032 is 200mAh. They are both 3V batteries. So if you replace a 2016 with a 2032 it will work fine, and will last longer, but you need to make sure that it will actually fit in the battery holder since it's twice as thick.
The difference between the two is the 2032 3v battery is just one battery per package. The 2016 3v are sold in packages of two. Therefore, the 2016 would mean you would have 2 batteries to use. One to replace the battery that has died and one to save as a back up or to put in a second remote for your garage door opener.
2032
Each remote takes ( 1 ) coin style battery ( CR 2032 ) or equivalent according to the owners manual
The voltage and diameter are the same. The only difference is the thickness. You may have to adapt the battery holder.
2032 3V Lithium Battery
One can purchase the 2032 battery from Walmart where it is available for $11.54. One can also purchase this battery from Amazon, eBay, CVS and in the UK from Argos.
CR 2032 is one of the most common of the "quarter" sized batteries, and retail for $1.80-$2.00 each most places.
tomorrow.
CR 2032, 3V lithium battery
The voltage and diameter are the same. The only difference is the thickness. You may have to adapt the battery holder.
CR 2032