Actually, when it comes to birds, it's not always true that males are more beautiful than females! I know that birds of prey the two sexes are almost indistinguishable, except that females are larger than males.
In the parrot world, many species (not all) the sexes look the same. Conures, macaws, cockatoos, pionus, senegals, amazons.... for the most part, these species (and others) cannot be visually sexed and you need to DNA or SS the bird.
And then there are eclectus. You wanna guess which one is the hen?
http://37.media.tumblr.com/tumblr_lxhrarjGln1r9xr1to1_500.jpg
Cross-bred and hybrid, to me, are the same thing. She is neither. Hybrid would indicate her parents are two separate species - i.e. one was a cockatiel and the other wasn't a cockatiel. She's a pure cockatiel. Not mixed with another species.
If it helps any.... a hybrid is like breeding a tiger and a lion together. With cockatiels, it would be like breeding a cockatiel to a cockatoo.
And a mutation is like the white tiger vs the normal orange tiger. It's not a hybrid, it's just a simple color difference.
Your hen is not a normal hen, she's the pearl (aka opaline) mutation. The pearl mutation is what gives her the spotted appearance with the brighter colored face and the tail feathers that are clear or lightly marked.
Here's a photo of a normal hen.
Here is a photo of a pearl hen, with her father behind her. Her father is split for the pearl mutation. (he has one gene for pearl, if he had two genes for it, he'd be a visual pearl, but he's not)
