The most efficient and economical cross is after a lead/fake. The distance the cross has to travel is across your chest from the back. That makes it really slow. If you were to just throw it you would have two problems.

Telegraphing. It's really hard to throw a cross with power if you don't give it leverage and space. Thus a lead/fake is prefered before the cross.

Slow. Now your rear fist has to travel not one arm length, but two. If you don't disguise it like after a lead/fake, anyone can see it and counter/parry your cross.

The cross is also a long-range weapon. Prefered use would be from a distance. If you're in-fighting a lot, I suggest using the uppercut or hook.

No, the cross is not another version of a hook. It's basically a straight done with the rear arm. It travels in a straight line with a lot of force due to distance and great leverage.

Back to your question, it can be called a "rear straight" but cross is a better name as everyone knows it by that name and in detail, a straight and a cross is different.

Assuming you're in an south-paw position.
A lead straight makes your body aligned in one line, whereas in a cross your right foot will be in front and your left fist will be out. Now in if you did a lead straight, your right foot and right fist will be in one line and your chest won't be exposed. In cross, your chest will be exposed to your opponent.

I'll go find some pictures for you, right now I'm kinda busy.

-Taison out

http://lannamuaythai.com/thaiboxing/0000pr02l00047u_techniques__the_hands.html

Scroll down and you should see the cross. That's how it's done in MT and I when I did boxing I did it this way.

Note: They call it a straight but I disagree as I follow BL's idea of how a straight is done with the lead arm. But still a straight is a straight. Now see the picture above the cross, that's how a lead straight should be done but more shoulder put into it with more power, not a snap punch like a jab. It's a hard punch, where you commit much power into it.

-Taison out

Ah, thanks taison.

You're welcome.

-Taison out

Cross - can't remember where I heard this, and am not sure how true it is but:

Face a partner, have them stick out a jab, you stick out a cross. The cross will cross over the jab and this is useful to recognize for counter punching

No no, cross a straight. The jab isn't commited, thus will lead you into him. Like a bait. I suggest doing it on signs that he will fully commit himself. Remember, many if they see that their straight lands the first time, they won't hesitate to do it again and again. Take that oppurtunity, unprotect you face and when you see it coming, hit him with a cross. Guaranteed KO.

-Taison out

Thats if you are still standing from his crosses.

Taison, how do you like to use punch-elbow combos?

???

Come again please?

-Taison out

I think he means you throw a punch and then you throw an elbow, by the way he wants to know in what situation do you like to use them them