Yes — “proj” most likely indicates a projector lens. The 135mm marking is the focal length, not the projector’s throw distance. In a projector, the lens works like a camera lens in reverse: instead of forming an image on film or a sensor, it projects an image from a slide or other film gate onto a screen. So the focal length describes the optical properties of the lens and its relationship to the film/image plane, not the distance from projector to screen.

“Tessar” refers to the lens design itself: a classic 4-element, 3-group Zeiss formula. So this appears to be a Zeiss Jena Proj.-Tessar 135mm f/4.5 projector lens.