Chile has VWP, yet I still have the regular tourist visa stamp on my passport and must enter the USA with it. If I leave the country (USA) for a few days to go to Canada and then return, does a new 90-day stay period start running upon re-entry or is it also considered a temporary leave as with the VWP?
When entering the US on a B1/B2 visa you will not be given the same 90 days entry as for a VWP. The exact time you're giving will depend on the circumstances and the border official, but in general for a B1/B2 you are likely to be granted 180 days entry to the US.
If you leave to Canada and re-enter, then the border agent has the choice of either granting a new 180 day stay, or continuing your previous stay using a process called "Automatic Revalidation". Presuming your US visa is still valid then they could do either of these. If your US visa happened to expire before your re-entry then they will go the Automatic Revalidation path as that allows you to re-enter even with an expired visa.
Either way, presuming you are granted the standard 180 day entry, you will not be subject to any form of 90 day limit.