Defining Screentones
First of all, let's make sure we're on the same page when we talk about screentones.
The most common form of screentones we use are halftones. They're the teeny dots that make up the "gray" images in manga.
There are also linear tones, as well as other ways to creatively show gray, like ellipses and squares.
There's also "dither diffusion" or "error diffusion"--they're called different things in different places, but it means randomly placed specks of black that fade well from dark to light.
And of course, there are pattern tones, made with various techniques of error diffusion, ink, halftones etc.