Cross breeding chickens ?

For pure bred they have to be the same.
If they're different breeds the offspring will be a mix of both parent's characteristics.
Crossbreeds, mutts, barnyard mixes, no specific breed.

 

Pure breed is same breed + same breed. For example a speckled sussex rooster and a speckled sussex hen make pure speckled sussex chicks.
Mixed or crossbreed is breed + different breed. Like a RIR rooster and a BR hen you can call the chicks either RIR cross or BR cross.
The only exception I'm aware of (there may be others, you'd have to look into your specific breed(s)) is Ameraucana crosses. They've been dubbed Easter Eggers.
I hope that helps

 

To have pure bred chicks you do need both parents to come from the same breed.

If you cross two breeds, you have hybrids.

If there's more than 3 breeds in the mix, they're mutts (unless you go to the trouble of trying to get them to a standard of look, utility, or performance over the course of years...then it's a breed again...)

That said, if all you're looking for are more chicks to grow into eaters or layers, then mixed breed chickens are awesome! They tend to be very hardy (cross breed vigor) and have mixed up genes so you get more variety in size, colors, activity levels, laying ability, et al.

If you're crossing on purpose for more layers, it's best to get a rooster from a breed that lays well to cover your laying hens. Then you retain the laying ability.

Note some 'breeds' aren't. They're hybrids themselves, like the ISA Browns, Red Sex Link, Black Sex Link, Golden Comet, Ambers, et al.

 

But in dubbing them Easter Eggers you're still breeding for a purpose -- laying several shades of eggs! And they can have a real mix of genetics. I'd say the only reason they're not a 'breed' in and of themselves now is that they don't have a 'closed' gene pool and they don't have a standard to match.