Dispatch
Dispatch is the assignment of a real carrier to your car. A quote is only an offer to try. A booking can sit for days with no truck attached. Until dispatch, no carrier has the job.
Dispatch means a carrier has been assigned to move your car. You should be able to see that carrier's name, its MC or USDOT number, and the rate it accepted. A text that says "you're all set" is not that assignment.
What you should receive
Ask for a dispatch sheet, or the same facts in the order: legal carrier name, docket number, driver name and phone, pickup window, and the amount due. Check the docket on SAFER or the FMCSA Licensing and Insurance search the same day. Authority can change after the quote was emailed.
Before dispatch, the broker is still looking. The first available date you gave is the earliest you can release the car. It is not a promise that a truck will be there that morning.
How dispatch differs from a quote
A quote says a company will try to book the job near a number. Dispatch says a carrier took it. The price can still be re-quoted if the car is not what was described, or if no carrier will accept the old rate. RideShipper does not dispatch trucks. Companies that answer a quote request do that work, under their own authority.