When you are not sure and don't want to waste your time investigating, you can do &>/dev/null in bash and get rid of them both at the same time.
... But only in Bash 4. This doesn't appear to work with stock OS X (Bash 3).
Betty:srcs lelf$ perl -E 'say "out"; say STDERR "err";' &> out && cat out
err
out
Betty:srcs lelf$
GNU bash, version 3.2.48(1)-release (x86_64-apple-darwin12)