A #1 copper conductor will limit the voltage drop to 3% or less when supplying 95 amps for 200 feet on a 208 volt system. This size will allow the conductor to be loaded to 76 amps. 95 x 80% = 76 amps
Conductors are only allowed to be loaded to 80% or their rated capacity. If you need the full 95 amps then you would need to use a wire with a rating of 120 amps. 120 x 80% = 96 amps.
A 1/0 copper conductor will limit the voltage drop to 3% or less when supplying 120 amps for 200 feet on a 208 volt system.
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As with any electrical installation, the wire size used depends on the expected maximum current the wire will carry. That cannot be determined by voltage alone.
No a 208 volt outlet does not need a neutral. 208 volts is the line voltage between any two legs of a three phase 208 volt system.
A three phase panel will not give you 110 and 220 volts. A three phase four wire panel will, but not at these voltages. The nearest voltages will be 120 and 208 volts. The 120 volt is the wye voltage of 208 volts. 208/1.73 = 120 volts. A single phase three wire panel will give you 110 and 220 volts.
The size of conductor needed will be a #14. It should be copper and have an insulation factor of 90 degrees C. The fact that it is a three phase load does not enter into the calculation of the wire size.
A source of 208 volts can be obtained from any two legs of a three phase four wire 208 volt system. The two legs are classed as single phase 208 volts. The lead tags can be L1-L2, L2-L3, or L3-L1 all of which will give you 208 volts. Any of these lead tags to the grounded star point (wye) will give you 120 volts.