Normalization is a metric used to rescale the value in some range like 0 and 1. However, the outliers from the data set are lost. You should use this when you want all the parameters to be in the same positive scale. For example, you can use min-max scaling.
Standardization is the same but the difference here is we generate re-scaled value in terms of standard deviations. Standardization rescales data to have mean = 0 and standard deviation = 1. Most of the time we use standardization.
It depends upon the situation to situation. You must check the structure of your data. Then you should decide by which method you should go with. The rescaling metric is applicable to both dependent as well as independent variables.