If you want work in the image processing field, my first advice would be to try and understand various techniques, tools and algorithms used, understand how they work, where and why they are applied and what you can achieve by applying each of them to your input without actually trying to classify them into labeled boxes.
Unfortunately, terminology is not perfect and it is hard to reach a naming consensus even concerning high level concepts, let alone detailed techniques.
But, about noise and noise removal: First, it is important to understand that noise can appear in the image for various reasons most of which could be classified to:
- noise introduced by the sensor (camera, film, circuitry)
- "digitally" introduced noise (errors in transmission, lossy compression)
And I would say that noise removal could be part of both processes of image enhancement and image restoration. The opinions are based on my own intuition as somebody who's been working in image processing for a few years now, but:
If I got an image from a bad-quality sensor, or simply wanted to increase the details on any image obtained directly from a camera, I would call it image enhancement.
An example I saw and would probably classify as such is processing of satellite images. Usually, before processing the image, you want to enhance the contours and remove small intensity variations.
If something corrupted the image you got from the sensor and you want to revert back and obtain an image as close to the original, sensor-returned image, I would call it image restoration.
An example could maybe be trying to correct the images (frames) while video streaming, where you would want to handle the losses as much as possible and still display a (good) video.