[PA] Legality of using a brand name sauce of another restaurant?

If I were to open a chicken tender restaurant and only offered commercially available Chik Fil-a sauces (like the ones you can buy at a grocery store) then would I be breaking a law? If so, then how does the law distinguish between brands in this scenario? Like I noticed a lot of diners have random brands of sauces. If it is illegal for a restaurant to use another restaurant's brand of commercially available sauce then why would it legal for restaurants to use these random brands?

Please let me know if you need more clarification on my question.