Different powders will create different velocities at the same powder volume as well as different fouling characteristics. This has the potential to change group sizes and impact location. Even the change from old powder to new of the same kind, I would think, would have potential to change this.
On a side note, I've been the happiest with Triple 7, having also tried Cleanshot, Blackpowder, Pyrodex, and another one or two through the years. I am currently shooting FFF.
Having just reread your post, I see you are mostly asking about the change from FFG to FFFG. The answer is the same, yes it can. FFFG will burn faster and give a different velocity than the same amount of FFG.
