Stab stitching is when you insert needle straight down to the backing and pull it all the way through, then straigt up. I guess kind of like needlepoint? The problem with stab stitching is it doesn't make for a very attractive back, the stitches tend to be out of alignment. Some are quite good at it though. I only do it shen I can't get through all the layers with a normal quilt running stitch.
QAYG is "Quilt As You Go". A process where each individual block is quilted then joined together into a big quilt using sashing.