All these sensory tools share similarities in that they are a collection of textures and decorations to engage someone's hands. In the case of patients with Alzheimer's or dimentia, these tools can prevent self harm in the form of picking at skin. In people with autism spectrum disorders, these tools can help with some self-stimulating behaviors. So the type of sensry tool needed depends on the individual needs.
The following are how I define the projects I make.
Cuffs tend to be smaller cylinders that fit closer to the arm. They only have decoration on the exterior.
Mats are flat pieces meant to be laid on a table or lap. All decoration and texture is on one side, though borders may be added. They may also be "transformable," meaning that they can be turned into cuffs with buttons.
Muffs are larger cylinders that have decoration both in the interior and on the exterior. This allows both hands freedom to interact with the tool in a variety of ways. They also keep hands warm!
Beaded crochet
Puff, bobble, and popcorn stitches
Ribbed stitch
Shell stitch
V-stitch
Waffle stich
Bonando, Wanda. (1978). Stitches, patterns, and projects for crocheting. Harper Colophon Books. ISBN: 0-06-091095-X
Chachula, Robyn. (2011). Crochet stitches VISUAL encyclopedia. John Wiley & Sons, Inc. ISBN: 978-1-118-03005-9
Ellison, Connie (Ed.). (2018). Fiddle mats, muffs & cuffs. Annie's. ISBN: 978-1-59012-883-1
Haxell, Katie., Hodgson, Nicola., and Knight, Erkia (Eds.). (2015). 500 Crochet Stitches: The Ultimate Crochet Stitch Bible. St. Martin's Griffin. ISBN: 978-1-250-06730-2
Leinhauser, Jean. (2016). Embellishment stitch guide. Leisure Arts, Inc. ISBN: 978-1-4647-3885-2
Roberts, Luise., and Lodinsky, Heather. (2015). The Crochet Block Bible. Quarto Publishing Group. ISBN 987-0-7858-3331-4
Scharf, Bella. (1976). Illustrated patchwork crochet. Butterick Publishing. ISBN: 0-88421-052-9