I agree with Leo D., except that I would add that usually "snatch up" adds a slightly negative tone or even sinister tone at times.
1. Watch out or the boogie man will "snatch you up" if you don't close your eyes and go to sleep!
2. John "snatched up" the newspaper before I could finish the crossword I started.
A more neutral version with the same meaning would be something like this:
1. The school bus will "pick up" your children at 8:05.
(If you said "snatch up" here, it would sound like the kids are being kidnapped.)
2. The lawyer took the paperwork from the judge.
(If you said "snatched up" here, it would sound like the lawyer is mad at the judge for some unexplained reason, or
possibly that the lawyer is trying to keep something from the judge.)
Happy Writing!