I found an internet ad for 6/3 with ground metal clad.
I guess this cable uses metal-clad as ground.
Is this a safe way to wire 14-50 outlets?
If I chose to use this cable, I guess I have to connect a wire from the ground terminal of 14-50 to metal clad???
Short answer: yes it should be good cable for 14-50 outlet.
6/3 with ground means there are 4 wires inside the cable. 6/2 would be 2 conductors plus a ground. 6 AWG copper is rule of thumb rated to 60amp (long runs over 200ft you might have to derate the cable and go for next size up) For a 50Amp plug it's slightly oversized if copper unless you wanted the larger size for future proofing or long run or other issues. Just make sure it's copper and not aluminum since most receptacles are not designed for aluminum wire and remember the rating for aluminum at #6 is different and wouldn't handle as much currant as the copper version.
Metal clad is a generic armoured cable.
The armour is NOT used as a ground though it should be bonded to the electrical panel and outlet box through the connector used to enter the box. It should have a dedicated bare ground wire in the bundle already. I never really figured out why electrical wire says 3 wire when there are really 4 when you include the ground. It's like they forgot about the ground wire which I can understand makes things confusing.
Metal Clad is very similar to TECK cable (very popular in Canada)
The difference is the inner cables in TECK cable have another inner PVC layer of insulation between the bundle of cables and the armour and an outer PVC jacket over the armour too. Standard metal clad cable has a paper and/or thin plastic layer covering between the wire bundle inside and the armour layer, but it's not a full jacket insulation. (needed to keep the cables from rubbing on the armour). Because TECK has that extra insulation it's a bit more durable and reliable in certain extreme conditions. This type of cable was originally developed for gold mining at the TECK gold mine which is how it got that name it can be configured for hazardous location use with proper connectors and installation techniques but is still popular for residential use as it can basically go anywhere and replace a need for conduit.
Your alternative would be to run conduit and pull in the required individual conductors and ground wire through the tube and for a lot of cases this is better for a more permanent install. TECK is expensive, the connectors are expensive, and some people do not like the look of exposed TECK / MC wire if run on the surface. Conduit can be labour intensive and require skill to install though.
Yes this is safe to wire 14-50 outlets. In fact metal clad is a very good use case. If you need it in or through a wet location then you have to check if the specific cable is designed for wet.
The outer PVC jacket is optional in metal clad. MC is kind of a generic term. TECK is a very specific version of an armoured cable with specific required features (outer PVC, armour, inner PVC)
MC cable can have copper or aluminum conductors, it can have paper or plastic between the cable and armour, the insulation on the cable is usually one of THHN or THWN and the ground can be bare or insulated so you would have to look at the specific spec sheet of the metal clad cable you are buying to know how it was made.