Noise in the jargon of digital imaging describes a lack of uniformity seen in an image. This is akin to “grain”, a similar effect, different cause, common to film photography.
In digital photography, the lens projects an image onto the surface of a digital sensor that is covered with millions of photosites. During the actual exposure, light energy is converted to an electrical charge. This action happens independently in each photosite. The resulting charge is feeble, thus an amplifier built-in to each site boosts the charge independently. The amount of amplification applied at any given site is based on the ISO setting and the brightness of the image playing on that site.
Now all the amplifiers should work alike, but each operates at different efficiencies, so the amount of amplification applied will be slightly dissimilar. This is the root of what plagues us as “noise”. Noise is worse when the image projected by the lens is feeble. Under these conditions, the amplifiers are turned up high. The result is a lack of uniformity due to each site applying differ amounts of gain.
As to noise differences between different mounted lenses: We use the f-stop system as a means to compare image brightness, lens-to-lens. In theory, any lens set to the same f-stop should yield an image with identical brightness. The problem is that the f-stop is a mathematical computation. We divide the focal length by the working aperture diameter to derive the f-stop. This method does not take into account light loss due to the fact that the glass is not flawlessly transparent. The f-stop does not take into account light loss due to reflections off the polished glass surfaces. In other words, the f-stop system is imperfect. Some lenses are calibrated using a “T-stop”. This is an f-stop with improved accuracy based on actual measurements made of image brightness.
So to explain your experience, more noise from one lens vs. another. Likely the lens with more noise projects a feebler image and the camera’s chip logic is turning up the amplification to mitigate. You are thus seeing the effect of uneven amplification. Additionally, your camera yields a JPEG image. This is a file compression algorithm that will under certain circumstances promote more noise.