Notches I use, what I call them, and how I typically employ them. If I'm calling them by the wrong name let me know, I just call them what I was taught.
Top face, _\ I cut the top about 45 degrees. General purpose lets get this guy on the ground notch
Bottom face/modified Humbolt, not sure which characters to use to make a picture but the horizontal cut is one top, and the face cut is on the bottom. I use it when I really need the tree to stay put when it is on the ground, it can't come backwards, or I really need it to clear the stump, tops, or all of the above.
Double face/wide notch. > I use it mostly on tops we are pulling hard on. It allows me to pull the trigger with the cut when the spar has returned to a more natural position once over center so I go for less of a ride and impart less shock load to the spar if roping it out.
Humbolt. Old school style humbolt with the face being a vertical bore cut with two parallel cuts at the top and bottom. I use it pretty exclusively in live trees that are coming down whole where accuracy is critical. Very easy to steer with the back cut, very easy to gun sight with a spotter. Will also use it on very hard leaners where a bored back cut is needed. I often use it when risk of barber chair is extreme.