NACS
NACS, the North American Charging Standard, is the charging connector Tesla designed. SAE International is standardizing it as J3400, and it works for every charging level, including Tesla Superchargers.
The Department of Energy's Alternative Fuels Data Center notes that several carmakers announced plans to adopt the J3400 connector, giving non-Tesla EVs access to Superchargers. Teslas come with a J1772 adapter for other Level 2 stations.
Charging time depends on power, not plug shape. See the Tesla Model Y and Tesla Model 3 pages for EPA charge times, or the FAQ on how long a Tesla takes to charge.