Yes both those groups qualify and do several others. Visit this page for a complete list of qualifying jobs:
budsgunshop.com/catalog/qualified_professional_discounts.php

You absolutely do and thank you for your service! I'd go to Special Deals and then Qualified Professionals to see the items that are discounted and if you want one, I'd submit the information required to get the discount.

budsgunshop.com/catalog/index.php/cPath/2083_1799/Special+Deals/Qualified+Professional+Discounts

Enter the special deals tab towards the top of the page, then follow prompts to see if you qualify for the discounts. You must provide proper credentials to be able to purchase guns or other available products.
Who qualifies for the Qualified Professional Discount?
Many major manufacturers offer discounts to a large list of individuals they consider Qualified Professionals. Although commonly referred to as Law Enforcement or LE discounts, these discounts are actually also available to many other types of Qualified Professionals, including.....
Active or Retired Military personnel - all branches
National Guard personnel - all branches
Military Reserve personnel - all branches
CAP - Civil Air Patrol
Fire Fighters - including volunteers
Paramedics and EMTs
TSA Employees
Commercial Pilots
Federal Flight Deck Officers
Court Judges
District and Deputy District Attorneys
All sworn or retired Law Enforcement Officers - city, county, state, and federal
All Corrections Officers
State Licensed Security Companies
How to Submit your Credentials:
You can send us a copy of your qualifying credentials online by CLICKING HERE (Account Login Required).
What to Submit:
A current and complete (front and back) copy of your official identification. If you cannot send official identification, we accept LES forms or department letterheads stating employment. Please also include your driver's license if you use one of these two methods

Or, at the top of home page, click special deals. This will drop down the qualified professional listings. But you must qualify before purchase.

Yes, simply google buds guns qualified professionals discount. Then select the Buds page in search results. This will give you a click here option to submit your credentials. Retired military are eligible. This is the easiest way I can explain to help, hope it works for you.