Sorry if I'm confusing what you're confusing.
But I think you're confusing probably because the "cross" equivalent Spanish word has the same multiple meanings in it.
For example, let's think about the English word, "right."
The opposite of "left" is "right" or 右 in Japanese.
The opposite of "wrong" is "right" or 正しい in Japanese.
The same spelling English word "right" has at least two different meanings, you know? And they may not be interchangable in other languages.
When you say, "Turn right at the next intersection," you can say 次の交差点を右に曲がってください. But you cannot say 次の交差点を正しい方に曲がってください.(Turn to the correct(right) direction, which might be left according to the situation.)
If you dare use the same word 右 for "right(correct)", it brings about fatal mis-communiccation, you know.
Is this clear so far? If you don't understand this, just forget it.
Likewise, "cross" has a lot of meanings.
You can check them by putting "cross" into the box at the top of this page, "English-Japanese" dictionary of WR, as gengo mentioned at #2.
The "cross" in the meaning of "hibridization" and the "cross" in the meaning of "two perpendicular intersecting lines" are just different in Japanese, which are 交配 and 十字, respectively.
Is it clear?
Hope this helps!