classical mechanics - Action and Action integral: Different kinds of variational principles

What are the difference between:

1. 
   

   the action $\int_{t_{1}}^{t_{2}}(L+H) dt$ that we use in the principle of least action, and

   
   


2. 
   

   the action integral $\int_{t_{1}}^{t_{2}}L dt$ that we use in Hamilton's variational principle?

   
   

References:

1. 
   

   H. Goldstein, Classical Mechanics, Section 8.6.

   
   


2. 
   

   H. Goldstein, Classical Mechanics, Chapter 2.