Let me start by saying that 'kill computer virus' is unusual to hear. One would typically say 'remove computer virus' as they are understood to be only files or data in particular places that allow them to control the machines behavior and are in no way actually alive.
According to Merriam-Webster, the words are synonymous. However a bit of history might give better context as to their common use (in the U.S., which the only first-hand knowledge I possess.)
The term 'generic' became most popular in the U.S. with white-label goods that were sold in stores cheaper than their brand-name competitors. The 'generic' goods were essentially without a brand or manufacturer markings on the label. These have since been largely replaced by brands that are 'owned' by a given store as the 'generic' products were perceived to be inferior. Brands like 'Members Mark' (Sam's club/Walmart), 'Kirkland' (Costco) and others have replaced the traditional 'generic' goods as the inexpensive alternative. In this situation, 'generic' implied that there was no company to which one could complain if there was a defect with the item.
In my opinion, 'generic,' therefore, has a mildly negative connotation to it, whereas 'general' or even 'generalized' (for those that prefer 'utilize' over 'use') does not. My company would never offer a 'generic' solution for sale as the presumption would be that it would be inexpensive and potentially inferior to a brand-name solution.
In answer to your final statement:
I want to show that the framework is normal, does it job, nothing fancy and that's about it.
I would use 'general.' Given more freedom, one might also consider 'simple', 'adequate', 'minimal', 'minimalistic' or even 'elegant,' depending on what other characteristics you might wish to convey.
I hope this helps...