If you apply for patent protection for a product, such as a drug, and another person produces the same product in other ways, is this an infringement? Why?

There is no infringement in applying for a patent. Only when you make the same product in other ways, the product is infringing, and its manufacturing process is not infringing, so it can only be said that the product is infringing. As for you, "any book about patents will say that patents can protect products or methods" means that you can protect the composition/structure of manufacturing methods or products themselves when writing patent application documents. The method or product itself here only refers to the method and product itself listed in the claims in your application documents. If there are thousands of ways to produce products, but you only apply for one, then you only have the patent right for this method. If you don't apply for the method, you will only have the patent right of the product. At this time, if someone else applies for the process of manufacturing a product in a certain way, then you can reproduce the product in this way, even if it is infringement. Of course, the other party's adoption of the above method is not infringement.