FIR difference equation vs convolution summation I'm sorry if my question is too simple, but I am self-studying FIR because we have to report it in our class. I am using the book of Proakis and Manolakis as reference. 

Under 7.2 Structures for FIR systems:


  In general, an FIR system is described by the difference equation
    (7.2.1)
  
  or evidently, by the system function 
  
   (7.2.2)


Under 7.2.1 Direct-Form Structure:


  The direct-form realization follows immediately from the nonrecursive difference
  equation given by (7.2.1) or, equivalently, by the convolution summation
  
   (7.2.4)


I can see that they almost look the same apart from the bk in 7.2.1 and h(k) in 7.2.4. Question is, how are they different or related to each other? Sorry if you find my question too basic. Thank you in advance for the help!
I should have read further before asking this question! Anyway, I've found out that there are different ways to implement the FIR system as mathematically described in Equation 7.2.1 in the post above. Among these realizations/structures is the direct-form, which is the simplest to begin with. Equation 7.2.4 shows the transformation of the general equation in 7.2.1 in accordance with the direct-form.