It's both, really. Per your link:
The valve is designed to open when the oil filter becomes clogged or when the oil is too thick.
Bottom line, the bypass/relief valve opens in any situation where the filter media restricts the oil flow enough to create that 8 psi pressure differential.
Finding the psi rating of the bypass valve can be kind of a pain. It's published for some filters but not for others.
For example,
here is the oilfilterdata.com page for the Wix 51515, which is a common choice to use with the valve cover oil filter setup. You can see the bypass valve on this unit starts to open at 8 psi, and then is fully open at 16 psi.
But other filters are different. The Purolator L30257 opens at 20 psi and the Wix 51355 opens at 33 psi. That might be above some folks' comfort level.