The terms standardization and normalization are often used interchangeably. However, strictly speaking they do refer to distinct feature transformations.

Normalization

Normalization, also called feature scaling usually means scaling the data between 0 and 1. There are many approaches that can be used to achieve this. One common way is by

$x' = frac{x - x_{min}}{x_{max} - x_{min}}$

Standardization

Standardization transforms the feature to have a mean 0 and a standard deviation of 1. This is also called z-scoring and can be achieved by

$x_i' = frac{x_i - bar{x}}{s}$

where $bar{x}$ is the mean of the feature and $s$ is the standard deviation of the feature.