There is a big delta between being fired and being downsized; like core dumps. Some have backtraces, some don't.
I think you originally meant to say "laid off" versus "downsized" as downsized isn't related to the individual employee but to the company has a whole. Still though except for some background check by a government job or unemployment benefits I see little difference between being fired and laid off. Sure there are some differences but I wouldn't call it a big delta at all.