'prog > log' would more accurately be written as 'prog 1> log' as it is redirecting the standard output, which is assigned to file descriptor 1, to a file called log. Standard error is associated with file descriptor 2, so to redirect it use 'prog 2> errLog'.
Putting this together you could do something like...
prog 1> standardOutputLog 2> standardErrorLog
or maybe send them both to the same file...
prog 2> tmp 1>&2 (or prog 1> tmp 2>&1)
You might find this link useful:
http://duplex.hypermart.net/books/bsd/265-267.html