I'm trying to decide if they mean the same thing. Obviously they do, in that the outcome is the same (if we ignore the option of walking on the flower beds). There is also a strong hint in the positioning of the Path version – it's on the grass. 'Oi! Not 'ere. Can't you see the path?'
But 'Keep off the grass' comes with baggage: bossy park keepers, school rules (at my school, the teachers and prefects could walk on the grass).
'Keep to the paths' mostly works, except that some of the paths are grass... which would stop robots in their tracks if they've also seen the 'keep off the grass' version.
I like the way Paths is capitalised, by the way - a multi-faith notice.