Broadly, AE is a layer-based compositor (a tool for combining multiple still and moving images) which also excels at motion graphics.
Smoke is an all-in-one editorial finishing system, with an NLE and modules for keying, painting, color correction, graphics, effects, and compositing.
Shake is an old node-based compositor, which has been largely replaced in the industry by NUKE.
If that raises additional questions for you, I'd be happy to try to answer them.
Principal & Designer at Keen Live
Motion Graphics, Widescreen Events, Presentation Design, and Consulting RenderBreak Blog - What I'm thinking when my workstation's thinking
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