What is the power socket voltages in America?

You are correct that if the 120v supply is derived from a three phase source, the line-to-line voltage of the source is 208 v.

But most domestic supplies in the US are not derived from a 208v three phase supply. Instead, the three phase distribution voltage is supplied to single-phase transformers with 240 v secondaries, and with a mid-point tap to deliver 120v. The voltage of that three-phase primary distribution varies regionally - the most common is probably 4.16kV line to line (2400v line to neutral).

The single-phase step down transformers can be rated for either line-to-line or line-to-neutral primary connections. Most distribution utilities choose to rate their transformers for line-to-neutral connection because that means that the transformers only have one primary bushing - and when you are buying thousands of distribution transformers, the difference between single-bushing transformers and two-bushing transformers is real money.

This makes is possible to supply 120v for ordinary receptacle service in the home, while also having 240v available for major appliances such as electric ranges and water heaters..

Three-phase 208 V is usually only supplied to some larger commercial and residential buildings. Smaller buildings and some large buildings are supplied single-phase 240 V from transformers that have a center tap secondary that is used as the neutral. Some utilization equipment is made in both 200 and 220 volt models and some equipment has a wide voltage range rating for use on either 208 or 240 volt systems.

Standardized at 120 V. Electricity suppliers aim to keep most customers supplied between 114 and 126 V most of the time. 240 V/60 Hz used for heavy duty applications such as air conditioners, clothes dryers, stoves, ovens, and water heaters. Buildings with more than two branch circuits will have both 120 and 240 V available. Type B outlets are now required by code in new construction and renovation. A T-slot Type B is rated for 20 amperes for use in kitchens or other areas using large 120 V appliances.