It's imprecise and there's overlap. However, to me (U.S. native speaker): 1) "To spot" suggests that you are actively looking and trying to find something specific. 2) "To notice" suggests that you're just passively watching, and suddenly became aware of something. "What was the street number of that house we just passed?" "I'm sorry, I didn't notice. I wasn't looking for street numbers." "Well, see if you can spot one, so we can get some idea of how close we are to #605." "Hey, I just noticed that we crossed Division Street. Does that help?" "Yes, it does. Try to spot Washington Street, that's the last big street we'll be crossing, then start watching for house numbers."

hi! from that word, it gives the same meaning or similar. but if you will eradicate the "to" they are still similar but it sometimes it will matter on how you used the "spot" and "notice". i hoped this will help.

Thanks, Tony

As I see it, the primary difference between "spot" and "notice" is the way it happens. "to spot" is entirely visual, almost a synonym for "to see". So it is direct and instantaneous. "to notice" can include other sorts of sensing, and suggests some amount of deducing is involved too.