Average Power Versus Real Power
In a steady-state circuit, if you average the "instantaneous power" over a cycle, you get "real power"... so yes, they are the same. 



Furthermore, this is how power meters work, to show what the real power consumed. They average the instantaneous voltage and current (vectors) over a few seconds.

If you know what power factor is, see this answer for more details:
https://electronics.stackexchange.com/a/50034/16096

edit:

unless you are taking about some appliance like an air conditioner.. whose power consumption changes as it turns on and off.. then the "average power" would be averaged over the day