Disclaimer: I am not the best at making visually distinct character faces myself; I am also on this particular journey. I've noticed that, for me, 'same face' syndrome tends to happen when I don't have a solid concrete idea, or reference material, for what a particular character should look like. If it's just 'face shaped with blonde hair' vs. 'slightly rounder face shape with brown hair', you're going to get a lot of 'same face'.
One thing that does seem to help me, though, is picking out what various art friends of mine and I call a 'face claim', aka pick an actor or other person to serve as specific facial reference for a particular character. Like, who would you choose to play your character in a movie? That's a face claim. You can have more than one face claim, too, like if you like one actor's nose, and someone else's eyebrows or whatever.
And from there, you may attention to THAT PERSON's specific features for your character. How does their nose look from this angle? What do their eyebrows do when they scowl, or smile, or are afraid? Having specifics helps.
Repetition also helps, especially when you're getting comfortable with a new character. I've noticed character faces sort of 'solidify' in my mind/drawing style when I have a better idea of who they are, what their defining features are, and the sorts of expressions they frequently make.
And yes, some characters will just give you hell and remain obstinate about being drawn for long periods of time. Them's the breaks of being a character artist. 