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A standard normal distribution has a mean of zero and a standard deviation of 1. A normal distribution can have any real number as a mean and the standard deviation must be greater than zero.
No, they are rarely the same.
No, the normal curve is not the meaning of the Normal distribution: it is one way of representing it.
Mean and Standard Deviation
Because the standard deviation is one of the two parameters (the other being the mean) which define the Normal curve. The mean defines the location and the standard deviation defines its shape.