What is a "Junior Faculty" position?
Generally it would mean a tenure track assistant professor position. There might be exceptions, but for Columbia, I'd expect it to mean just that. 

But they might even be willing to entertain a lower level (non tenure) or higher level (associate professor) position for the right person. I can't think of any other reason for a US university to be non-specific. 

But even an associate professor offer would likely come with some probationary period prior to granting tenure. Probably two years or more, but less than seven. 

Contrast it with "senior faculty" position. Here it would mean a full professor, even a distinguished full professor or someone able to take over a leadership role.