Shen uses a dependently typed Sequent-Calculus based Type System (SCTS). It uses type rules vs. type classes, and type checking is optional, you can turn it on or off. Haskell's type inference makes things a bit simpler, and is a battle-tested static type system with excellent type inference which lends itself better for functional programming and large-scale software engineering (for the moment). Shen's TC is more expressive, but requires more effort.
Aditya Siram has some old but goody YT videos on Shen.
I'm an idiot. I looked at this page: https://shenlanguage.org/TBoS/tbos.html many times, tried clicking on the table of contents, realized that chapter titles are not links, and went away thinking it's only the ToS for promotional purposes. I only realized that the page numbers are links just now. To my defense, they don't differ in color that much and lack the underline that often marks links. Still, a HUGE facepalm :D Thanks for mentioning this and making me realize my own stupidity :)
If you have any questions check out the Google Groups (no Groups comments!) for Shen. I am eager to see the 5th edition, and I will probably buy the print version.