Budget has corporate locations where they service, but I believe they also use some 3rd parties throughout the country. Penske is in-house; they are the best run of all the moving truck lines and typically charge the most for that reason. Budget can be very hit and miss. They use a lot of "dealers," as they call them, sort of like a franchisee, and they aren't known for caring much about the condition or cleanliness of the truck, just getting it on rent.
Source: Our family had a Budget Car & Truck Rental franchise; we owned our cars and rented the trucks for corporate, receiving a rev share. We actually cleaned the trucks (almost always came in filthy) and made sure they were roadworthy. Did my share of running trucks due for service to the corporate maintenance facility to pick up recently serviced ones in exchange.