G64 is set by default.
G61 visits the programmed point exactly, even though that means temporarily coming to a complete stop.
G61.1 stops after each move.
G61/61.1 AFAIK are the same (cradek)
G64 without P means to keep the best speed possible, no matter how far away from the programmed point you end up.
G64 P- means that it should slow down as required to get no more than P- away from the programmed endpoint. if G20 is in effect when you program G64 P-, then the P-number is in inches. If G21 is in effect when you program G64 Pn, then the P-number is in millimeters
In addition, when you activate G64 P- it turns on the "naive cam detector"; when there are a bunch of G1 moves that are less than P- away from being colinear, they are collapsed into a single linear move. this improves contouring performance.
The back plot in Axis will not show the exact path the tool takes when going real fast because to draw the backplot, axis only samples the path approximately 50 times per second. there's no guarantee that one of the samples will be exactly at the corner point, even in G61 mode. When it's not, it looks like the path deviated from the exact path. It's one of those unavoidable things and it's a problem that grows worse when you've got something complex loaded and axis is bogged down when zooming or rotating... or going 400IPM