Here's where I think the main difference is between RDWC and UC. With an RDWC, the water just needs to be cycled through the system so that nutes/pH is the same across the board. But UC has to have a minimum flow rate that ensures enough DO makes it through the entire system before it dissipates. The "current" also has to be powerful enough to draw the DO water through the roots, not just pass them by.
The common formula for the right size UC pump is total gallons * 12 = GPH required
Example:
With a system containing 50 total gallons, circulating the total water 12 times/hour requires a 600GPH pump.
My current pump is undersized @ 400GPH in my 50 gallon UC system. However, because I have the stones going, the under current isn't as vital. So right now I'm running an "RDWC", not an "Under Current". If I increase my pump size to the correct size required for an under current, the airstones aren't as necessary, even though I'd still use them so that the roots get an abundance of DO. That's why when you look at the CC UC systems, they include an air pump. In theory, with a UC, the water pump should be powerful enough so that an air pump isn't necessary.