What is the difference between get down to brass tacks/business and cut to the chase ?Feel free to just provide example sentences.

Get down to business means "let's start working now" or also "let's stop with all of this extraneous stuff and start doing what we came here to do" (not necessarily business-related).

Cut to the chase means get to the point. It is most often used when someone is talking in circles and you want them to tell you more directly what they mean, or maybe you're just bored of a long-winded explanation and you want to hear the point quickly and succinctly.

They could mean the same thing in a business setting if you were in a meeting and you felt like your manager or co-workers were going off on tangents and needed to focus on whatever work you're trying to do, however this would be relatively rude to say. "Let's get down to business" on the other hand could be used at the start of the meeting and it would indicate there isn't going to be any "fluff", you're just going to start working.