The focal length of a lens does not change, not even 1 millimeter when you mount it on a camera. This is true regardless of the camera’s format.
Your kit lens when set to focal length 50mm yields exactly the same image size and angle of view as the borrowed. A prime lens is one that has a fixed focal length and it is unchangeable. A zoom lens has a variable focal length, in your case the kit lens is adjustable 18mm thru 55mm. Now the prime lens likely has more acuity than your zoom. This will be especially true if you operate them at the same f-number (aperture setting). The real question is, can you see a difference is acuity between the two? Likely the differences will be hard to spot unless you view the two images side by side on a huge screen or make big paper prints.
That being said, the borrowed prime operating a f-1.4 or f-1.8 has far greater light gathering power than your kit lens which will be operating at f-5.6 when set to 50mm. the difference is the prime is 3 stops faster i.e it allows in 8X more light when set to its widest aperture (f-1.4).
So what does the so-called crop factor tell us? The full frame camera sports an image sensor that measures 24mm height by 36mm length. Your compact digital has a smaller sensor. How much smaller? 24 ÷ 1.5 = 16mm and 36 ÷ 1.5 = 24mm. We calculate your sensor as 16mm height by 24mm length. Another way to say this is 1 ÷ 1.5 = 0.66 X 100 = 66%. In other words your camera is 66% of the size of a full frame.
What does that mean as to the size of an image taken with a 50mm? Both deliver the same image size however the larger full frame (FX) will show more room around the subject because the sensor is larger. In other words, the angle of view between a full frame and compact digital (DX) is different. The FX angle of view with the 50mm is 40° and the DX angle of view is 27°. The difference is 40 X 0.66 = 27.
For my part, I wish the crop factor would go away. It is only important to those folks who use a full frame and know all about how it images with different focal lengths. Then they can apply the 1.5 factor to see what focal length on a compact will deliver the same angle of view. I think this is not particularly important to a fellow who never used a full frame.
The thing to learn is “how do various focal lengths image on my camera.