material vs atlas vs decal vs filter vs texture generator vs mesh based generator

I assume you are referring to the graph templates. Each is just a starting point for a different type of graph for different purposes.

If you twirl open the Template Details for each and scroll down you will see a description of the use for each template, many of which are appropriate for specific uses within Substance Painter, along with the outputs that will be set up. In addition, some set up inputs that will be required for their use.

https://helpx.adobe.com/substance-3d-designer/substance-compositing-graphs/creating-a-substance-compositing-graph.html

A description of those in your list can be found in the Painter documentation
https://helpx.adobe.com/substance-3d-painter.html

In short
Material - a group of textures that combine to form a surface material that can be applied for rendering. In Substance these are usually procedural so can be edited with controls and are recalculated at the required pixel density.
Atlas - a group of objects that can be scattered on a surface

Decal - A material designed to be applied to a surface in one spot e.g. a logo. or stain, drip etc In Painter any material can be applied as a decal

Filter a graph that acts on an input to produce an output

Texture generature - a graph that produces patterns or noises or full textures procedurally

Mesh based generator - a graph that uses input maps baked from teh mesh such as curvature, position etc to affect how it generates the output. As an example, that allows the generation of edge damage on the model, without having to paint along the edges.

Dave