The clipper creek is three wires with Hot/Hot/Ground, no neutral. There's 240V between the two hots, and 120V from each of those to ground, but under normal operation there's no current on the ground wire. A 10-X device is Hot/Hot/Neutral-Ground, a 6-X device is Hot/Hot/Ground. Electrically the third wire is mostly the same, but the former the device is allowed to draw unbalanced current from the hot legs and return the imbalance through the third wire, the latter must draw and return through the hot legs only, the ground is only for safety.
You can swap out the 10-50 for a 6-50 by changing third wire to ground, but there are code implications in the marking of the wire and which bus it is on if there's a subpanel in the mix.
Please do not give people this incorrect information!
A 10-series device is a line(hot)/line(hot)/neutral device, not "neutral-ground" and electrically they're not "mostly the same" especially when subpanels and/or detached structures are involved. The grounded circuit conductor (a/k/a "neutral") and equipment grounding conductor (a/k/a "ground") are two distinct items. The *only* place they are one and the same is the bus bar in one single service panel from any power company connection. Everywhere else they are separate (minimal exceptions apply for older outbuildings and such, I won't cover them here).
While it will work to do as you say, it is not safe in many circumstances to simply "change the third wire to ground"... There are key safety reasons the code has eliminated all combined grounded/grounding systems, for branch circuits in 1996 and for detached structures in 2005/2008. For example, if a neutral conductor fails between the service panel and a detached garage subpanel, and the charging unit's ground in that detached garage is connected to neutral, then unbalanced return current for that subpanel can return to the service panel and transformer through a person touching the metal case of the device and standing on the floor. It happens more than you might think.
The only safe and legal way to do this is to open both the receptacle and the panel to which the receptacle terminates, ensure the former neutral wire is moved to a bus with all the grounds (in the service panel this will be one and the same, otherwise it will be a separate electric bus), remark the wire with green tape on both ends, then install the 6-50 outlet. Note that remarking a white wire as green is only legal per code when it is part of a multi-wire cable assembly, but it's something many inspectors will pass anyway, as long as it is clearly marked green.
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Again, I'm clearly the least educated of your guys w/r to this stuff, but these diagrams seem to suggest the only difference between 10-50 and 14-50 is the ground protection.
Correct. The 10 series receptacles were WW2-era connections, grounding appliances using the neutral on 125V/250V appliances. The belief was that is was relatively safe because at the time, neutral and ground were mixed interchangeably. However, certain failure scenarios created significant harm for humans - shocks and death. I can recall getting one hell of a shock when I was a child at my great-grandmother's house because I ended up forming the return path for current on a broken neutral for her oven clock via the kitchen sink. That would not have happened post-1996 NEC.