Grab describes a kind of action - to take hold of something roughly, without care or gentleness. Snaffle describes more an attitude when taking something - to take something selfishly, without considering that others might want some too. She grabbed the cake so it fell apart in her hand. She snaffled all the cake so there was none left for me.

"Snaffle" is a fairly colloquial word. There aren't many situations where you would use it. "Grab" is a standard word in English. If you simply replaced "grab" with "snaffle", your sentences would sound very, very funny!

Not at all! 'Grab' is a very common everyday word, meaning to to take in a rough, careless way. 'Snaffle' is a very unusual colloquial word, meaning to take something for yourself so that another person might want. All native speakers use the word 'grab' in many situations, whereas I would guess that 90% of native speakers have never used the word 'snaffle' in their whole lives. As Peachey says, you would sound very funny indeed if you used 'snaffle' as a substitute for 'grab'.