I don't know if you mean exactly this, but I see a lot of people referring to Normalization meaning data Standardization. Standardization is transforming your data so it has mean 0 and standard deviation 1:
x <- (x - mean(x)) / sd(x)
I also see people using the term Normalization for Data Scaling, as in transforming your data to a 0-1 range:
x <- (x - min(x)) / (max(x) - min(x))
It can be confusing!
Both techniques have their pros and cons. When scaling a dataset with too many outliers, your non-outlier data might end up in a very small interval. So if your dataset has too many outliers, you might want to consider Standardizing it. Nonetheless, when you do that you will end up with negative data (sometimes you don't want that) and unbounded data (you might not want that either).