Ask HN: Will a B.S. in _Software Engineering_ hurt my chances for the Big N?

All of the Big N requirements say "Computer Science" B.S. needed. Is Software Engineer the same thing as Computer Science to corporations? Should I be wary of being pigeon-holed with a Software Engineering B.S.? Will it make no difference from an employment standpoint?

I ask this because I am a prospective 2nd Bachelor candidate at a California UC and they only offer Software Engineering as an option.

Thanks!