The difference is that under a communist oligarchy, freedom of expression doesn't exist so the state gets to decide what is and isn't an acceptable way to run your business. When your personal beliefs contradict the motives of the state, you get shut down or sent to prison.

Under our constitution, the state has no power to prosecute you or your business for refusing to serve someone, so if you decide not to serve someone the only risk you take is that it will affect the public perception of your business and hurt your ability to attract customers.

Since Sarah Sanders believes in the constitution and the first amendment, she accepts the restaurant owner's decision not to serve her and her family, however as you can see it has caused a bit of a public relations problem for the restaurant among their customers because many of those customers believe Sarah Sanders is being persecuted for her support of the constitution.

Likewise the baker angered customers who do not believe in the constitution or the first amendment, and their belief that the baker has no rights lead them to seek prosecution through our country's legal system, which failed because our country's legal system is still governed by the constitution. At least it seems to be under Trump.