Adding noise definitely is dithering when you use it to prevent too apparent banding which is caused by sparse brightness quantization levels in the image displaying system. Dither means the added noise, when the noise is added intentionally to make the sparseness of the quantization levels less apparent.
The dither, of course, can be a deterministic, even repeating quantity as long as it does not correlate with the variations of the too sparsely quantized thing. For ex. black & white printing of grayscale photos use regular dithering pattern (the raster) which rarely correlates with the photographed content. But when such correlation occurs we can see very disturbing interferences (for ex moire patterns).
Dithering has got numerous forms in different technology areas. Read this Wikipedia compilation of the subject: https://en.wikipedia.org/wiki/Dither
Dither can as well be randomness of placements and positions as random variations in signal levels. The linked article claims that the original form of dither was the mechanical vibration in WW2 aircrafts. It reduced calculation errors in 1940's mechanical firing and bombing computers.
An example of image dithering with noise
Both halves of the next BW photo are posterized to only 6 brightness levels. Both halves have also got in Photoshop a few percents of noise. Both halves look quite equally noisy. The half above the diagonal has no large bands, but the lower half has large bands which looks disturbing.
The difference is this: The upper half got its noise before the posterization. This dithers the sparse grayscale quantization effectively. In high zoom in it's still banded, but the bands are so small that the smoothing caused by distant looking partially restores the missing levels. The lower half got its noise after the posterization. That's only adding noise, it's not dithering.