Rivalry
Etymology
From Latin rivalis "one who uses the same stream as another," from rivus "stream, brook." Rivals were originally neighbors sharing a watercourse, forced into competition over it — the surprise is that rivalry is rooted in a shared resource, not opposed goals.
noun · /RY-vuhl-ree/
An ongoing competition between people or groups for the same prize, status, or ground.
What it names
A handle for a competition that has become a relationship — where the other party’s existence shapes and sharpens your own.
Example
Their rivalry pushed both scientists to work that neither would have reached alone.
Related idea
Distinct from enmity: a rival wants to beat you and often respects you, sometimes needs you; an enemy wants you gone. Rivalry can be generative and even affectionate, whereas enmity aims at destruction, not victory.