Presence mode, as the name suggests, is based on detection of presence of devices around a Wi-Fi Access Point. If a device's signals are detected and picked up by an Access Point, he or she is present in this zone/area .We won't be able to track the exact location of the mobile device but it's often good enough to have zonal information (for cost reasons)
Triangulation mode is based on multiple Wi-Fi Access Points, at least 3 but ideally 5, triangulating the position of a device, very much like how GPS detects your device position outdoor. This would normally double or triple number of APs required.
As an example, you might need only 3 APs to track 3 zones in your site, but you will have a lot of blind spots or overlapped area, since a zone is pretty much circular (or close to it).
But if you add more APs, you will be able to triangulate the position, assuming those AP signals overlap each other.
Presence mode
Triangulation Mode