The object of protection of an invention patent can be a product (a thing) or a method (an activity).
The protection object of utility model patent can only be a product (a thing).
So the method patent must be an invention patent.
Products and methods are two different things. Products are things, they actually exist, and they are tangible. Method is a process, which is related to time, and method is a process with time.
For example, if you invent a pen, it will be a product patent when you apply for a patent.
For example, you invented a method of making a pen, which is a time-related process. When it applied for a patent, it was a method patent.
Sometimes, an invention patent can contain two different types of inventions: products and methods.