They are both synonyms. (falling down)
There is a subtle difference though.
摔 - Has a more 'slipping' kind of implication. Like slipping off a cliff or on a banana peel.
跌 - Has a more 'tripping' kind of implication. Like catching your foot on a rock. (falling straight down)
Those are the only differences and because it's really subtle, no one would correct you if you prefer the use of one over the other. Helps to know though !. (^____^)
edit :
There are some (rare) instances where you cannot substitute one for the other.
Falling off a balcony you must use 摔。 It's strange to say 从阳台跌出去, but it makes sense if you say 从阳台摔出去。My guess is that even though it's a balcony, it's from a high place (like a cliff) and so must use 摔。 Probably helps to think that most balcony accidents start by someone 'slipping'.
跌 is also always used in an 'accident' context.摔 can be intentional.
eg.
我们一起摔到了 = O
我们一起跌倒了 = O
我把他摔到了 = O
我把他跌倒了 = X (has to be accidental)
我害他摔到 = O
我害他跌倒 = O (It's your fault, but still an accident)
Which is why wrestling is called 摔跤 and not 跌跤.
Really though....no one will tend to correct you. Just take note of the 2 examples I gave you and you'll be fine. (^____^)