Is there a different rate for round trip rides?

No, there is not with rideshares and on-demand transportations

For rideshare services like Uber and Lyft, there are usually no concepts of round trips.  They function on an on-demand basis, so you request a ride when and where you need one.  When you reach a destination, you would simply request another driver for your ride back.

With that said, you can "schedule" rides, so you could theoretically schedule a ride home, but there will not be a discount on the prices.

One thing you could do is to negotiate with the driver on the outbound leg. If this is a limo driver with a livery license, the driver may hang out until your appointment is done and give you a ride home.  Many drivers would prefer this, especially if the outbound trip was long. This will prevent them from making a "dead leg" trip to get home to his or her home area.

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC