Disclaimer: I have an engineering background.

I think this is a fair characterization of the two approaches.

I am currently taking a class by Strang co-taught with Alan Edelman (MIT/Julia) and Raj Rao (Michigan) that has a strong emphasis on applications and hands-on coding tasks (using Julia).[0] I am also making my way through CtM (thoroughly enjoying) and hope that they will release the video lectures soon as I think the lectures and CtM complement each other quiet nicely.

[0] Matrix Methods In Data Analysis, Signal Processing, And Machine Learning - https://stellar.mit.edu/S/course/18/sp17/18.065/