It's impractical to use a solid colour or shade of grey when printing manga and most other forms of printed media. Doing so would require using a separate ink to render each individual colour or shade. Instead most printing methods use a limited number of inks that are combined with the background and other inks using dots (other shapes) to render other colours and shades. For example a typical ink jet printer combines cyan, magenta, yellow and black dots to produce various colours, while the black and white pages of most manga use only black ink. Different shades of grey rendered are using techniques like hatching and screentones.
For example here's the cover of the first volume of the Yokohama Kaidashi Kikou tankoubon by Hitoshi Ashinano:
While it looks like the letters of the title are a solid colour, if you look closely they're actually made up of different coloured dots:
The cover was probably produced by taking the original artwork, overlaying the title, and then using some sort of halftoning process to produce something that can be reproduced the publisher's colour printing presses.
Inside, the manga is in black and white, and the use of dots and hatching to represent areas in various shades of grey is more obvious. When the manga was originally published it was in the manga anthology Monthly Afternoon, probably on cheap coloured newsprint. The printing process here doesn't support the fine, almost impossible to see with the naked eye, halftoning used on the cover of the tankoubon volume.
You can see the shadows on the character's arms drawn using a hand drawn hatching, while screentones are used to shade her pants, her hair and the guard rail in the background. You can also see where hand drawn details were added to the screentoned clouds in the background.
If solid greyscale fills were used in these areas it would require using a separate ink for shade used. Separate printing plates would have to be produced for each shade, and the printing process would have to ensure that each was applied precisely on the page so they don't shift relative to each other. This would dramatically increase the cost of printing of what originally was a cheap disposable magazine.
Alternatively, the greyscale filled pages could be halftoned or digitally dithered in a fashion similar to the cover. This would allow a single plate with black ink to be used, keeping printing costs the same, but the result would look pretty crude. The dots can't be as fine as used on the cover. On cheap newsprint they'd just bleed together to make the entire page black. With larger dots, it would end up looking like a fuzzy low resolution image. It wouldn't be anywhere near as good what can be produced through the judicious use of screentones and hand drawn shading.