Will I return at the same time I am departing on a round trip airline ticket?

Unlikely.

Of course, it depends on how far you're flying & how many simultaneous planes they have on that route, but for a short-haul...

You will either return after the arrival of the flight you departed on, so maybe an hour later than that - i.e. they need turnaround time to send it back out; or on a completely unrelated flight using a different plane, that will be part of a different turnaround, at a different time of day.

The only way you could return at the same time as your original departure would be if they run so many flights to that destination that there are two or more in the air simultaneously.

There may be a 6:15 return, but only if the airline ends their day with a plane at both ends. 6:15, depending on airport & local regulations, is likely to be the first flight that day for that aircraft - so if the carrier's normal policy is to get all craft 'home' at night then your first return flight will be after their craft gets to you from its home base.

It is possible to return on about the same time as you started, but almost never to the minute.

Many planes fly from an airport which they use as a base. So they fly from there and return to that airport. If your starting airport is not that base, you may find that your plane has come from the base and will return with you in it, and on your return flight you then will start on that base and return to the airport you left from, that flight may well arrive a short time before your departure time back when you started your journey.

With an 6:15 AM flight that is less likely than with later flights but with short flights and time difference between airports it is possible.

I used to fly Netherlands to UK regularly and both airlines I used to use had several flights going back and forth between the airports. Between those flights there was usually about 30 minutes, turn around time they call that, which they used to get the people off the plane, do some cleaning, get new food and such in and off course, to get the luggage out and new luggage in.
With that kind of serial connections you can easily find a few each day where the arrival time on the return flight is almost the same as the departure time on the outgoing. But you are often free to select an other flight, if there are more flights on the day.

On the other hand, if there is only one set of flights, you may not have much choice and your return flight may arrive when you would have been waiting for boarding already. Not the same time but not far off.

As noted in another answer, the times are unrelated, particularly if an airline has multiple daily flights between two cities or if the flights have multiple legs through a hub. Common examples can include:

• Out one morning and back at night the same day
• Out one morning and back at night on a later day
• Out one morning and back another morning
• "Red eye" - common in the US - east-to-west in the morning (arrive on the west coast early enough to make use of a large part of the day) and west-to-east late at night (arrive on the east coast early the next morning, so you can make use of the whole day...if you managed to sleep on the plane)

The timing is often based on productive time (whether for business or pleasure) being during the day and minimizing hotel stays. For example, if you go out on a Monday morning and come back late Tuesday night, you get two days at your destination with only one night in a hotel.

No.

Departure and and arrival times are typically completely different for outbound and return time, but are clearly spelled out when you book.

Depending on the route you often have multiple choice for each.