The simplest explanation would be that auto mode is more likely to increase your ISO setting in order to keep exposure time as fast as possible.

Compare these two images - both taken in low light. Camera was on a tripod & taken using a remote shutter release to try eliminate any shake. Camera set to Aperture preferred, focus was manual, so what changes is the ISO, with exposure time being automatically compensated to keep the overall light level the same.

The ISO was changed from minimum, 100 to maximum 25,600 to show the absolute extremes. Exposure time automatically changed from 1.3 seconds to 1/320th to compensate for the ISO difference. Images shrunk & saved as jpg, no other intentional changes.
Picture is just of a test canvas print on the wall, lighting very dim & orange, auto white balance for both.
50mm lens, Aperture f/2.2 (though that shouldn't be hugely important for this)
Click for full size

ISO 100 1.3s

ISO 25600 1/320s

I didn't even bother levelling the frame, though I did this so quickly I didn't notice until afterwards ;)

If you look at these in close-up, you can see how lifting the ISO too far is directly responsible for amplifying the noise level.
If you need to do this for very long exposures, 10s or more, then the camera's inbuilt software will run a noise-reduction cycle based on taking a short image after your main & use the two to attempt to compensate the noise. For short exposures, this doesn't happen, leaving you with all the noise.