This book provides a high level overview of many methods without (on a quick skim) really hinting at the practical usage. Basically this reads as a encyclopedia to me, whereas Nocedal and Wright is more of an introductory graduate course going into significantly more detail on a smaller selection of algorithms (generally those that are more commonly used).

Picking on what I'd consider one of the major workhorse methods of continous constrained optimization, Interior Point Methods get a 2-3 page super high level summary in this book. Nocedal and Wright give an entire chapter on the topic (~25 pages) (which of course still is probably insufficient detail to implement anything like a competitive solver).

Breadth vs. Depth.

Alg4Opt covers more topics, providing the motivation behind the algorithm, sometimes a basic derivation, and a concrete implementation. It has citations in the margin for more info.

Nocedal and Wright will go more in-depth on derivation, proving theorems, etc. Implementations are pseudocode, and fewer topics are covered.

Next time mention the name of the book first.

Numerical Optimization (Jorge Nocedal, Stephen J. Wright).