No, in an American restaurant, the business transaction is between you, the restaurant, and your server. You are explicitly given permission to refuse (extra) payment to your server, and the restaurant (to a limited extent) backstops that risk for the employee. You're going to have bad relationships (and experiences) with American restaurants if you make a habit of undertipping.
In an American retail or grocery store is my business transaction between me, the store and the cashier?
What's the difference between a server and a cashier? One walks between point a and b instead of standing in place? How much should I tip a cashier; 20% of the cost of my groceries?
If my grocery store has a hot bar of to go food that is packaged by the employee and handed to me to eat on their patio or take home. Should I tip that employee? If they worked at a restaurant they would tipped. My point is the waiter chooses to take less pay in hope of a tip, while the grocery store employee would rather know what their check is going to be and have stable reliable verifiable income. Wait staff don't have that. They make $0 on paper, they take the risk to avoid taxes, while the grocery store employee pays their "fair" share of taxes and social programs. While the waitstaff complains about tips and not earning a living wage.
Complaining about a job they chose when there is a multitude of jobs that you know exactly what you're getting paid based on your hours.
All this being said I do tip. I don't mind it. I find it hilarious when they spin the iPad around around to "answer a few questions" ie "please please tip me, I'm not gonna look or judge you but I am going to look and judge you and most likely passive aggressively spell and say your name wrong to show you why you should tip better!!"
Does the point of sale system ask for a tip? Is there a check with a tip line on it that you sign? Is there a prominent tip jar? Then: tip (or do business elsewhere). Else: don't.
You're missing the point. The existence of that line or that jar will change whether tipping exists, even though your relationship with that person hasn't changed at all.
So maybe it's not really a three way relationship in any of these situations.
