I've searched the answer which seems to be 1800W (120V x 15a) but it's not clear to me whether the rating is for each of the two outlets or the pair together.
So I would like to know: what is the maximum for each outlet and what is the maximum if both are in use simultaneously?
The limit is imposed by the circuit breaker, and is common to all outlets in a chain. There's no limit defined by the NEC as to the number of outlets on a single circuit.
So: the limit is for the pair of outlets and beyond.
For continuous loads (e.g. heaters) code maximum is 80% of the breaker value. For things like a vacuum cleaner, you can go right up to the limit.
There are restrictions that all occur simultaneously. You are limited by the lowest of these.
A NEMA 5-15 receptacle is limited to 15A per socket. A 5-20 receptacle is limited to 20A per socket.
A NEMA 5-15 duplex receptacle is limited to 20A per receptacle.
5-15 receps are allowed on 20A circuits if there is more than one socket on the circuit.
A 15A circuit is limited to 15A from all sockets and hardwired loads on the circuit. A 20A circuit is limited to 20 amps, ditto ditto.
Appliances which are continuous loads must be treated as 125% of their actual load, so a 12A appliance must be treated as 15A. This is the same derate as the 80% derate most people talk about. Think of it as 125% per appliance it applies to, not 80% for the whole circuit.
Underwriter's Laboratories publishes a White Book with their own requirements for devices. These are separate from NEC. For cord-and-plug connected appliances using a NEMA 5-15 plug, they limit current draw to 1500 watts (which they derive from 125V voltage and 12 amps, making it 80% of a 15A circuit).
No single plug-connected item is permitted to draw more than 80% of the rating of the circuit. That would be 12 amps for a 15 amp circuit and 16 amps for a 20 amp circuit. You will not find item sold with a 15 amp plug that draws more than 12 amps or an item with a 20 amp plug that draws more than 16 amps. However, there is nothing to prevent 15 or 20 amps of load from being connected through a power strip. Also, 15 amp outlets are permitted to be used on a 20 amp circuit. That would indicate that each individual 15 amp outlet or pair would need to be capable of 20 amps.
Edit: What is permitted is stated in the National Electrical Code, article 210. The use of 15 amp receptacles on a 20 amp circuit covered by Table 210.21(B)(1) and the 80% limitation is covered by paragraph 210.23(A)(1).
Re answer by Bryce
The main answer is direct and to the point, but the last part is not true.
The current / power rating applies to EACH of the outlets in a duplex receptacle. That is: you can draw the full rated current for the circuit from any one outlet in that circuit.
However, you must not exceed the maximum current rating of that circuit. If one outlet is drawing the maximum current allowed, then no other outlet on that circuit may be used.
AC voltage is the peak to peak maximum, so you can't multiply the current times the voltage with AC- you have to use the "RMS" or root mean square voltage which is about 62 volts when an outlet has 110V AC. So if you have a 20 amp breaker you must multiply 20 amps times 62V RMS to get 1240 Watts. The folks who say it's 1800 would only be correct if it was DC, which went out when Westinghouse used Tessla's AC to replace Edison's DC- about 110 years ago!
