**Negative numbers**  
When you subtract the mean, all differences will be centered around zero. So if you present your data in a barplot, the bars may suddenly be negative. However, how you apply standardization can have quite a different effect.

**Scale**  
When you divide by the standard deviation, the data will have variance and standard deviation equal to one. Hence the difference in scale.  

> My normalized data are normal (by definition...)

By what definition exactly? They just have mean $0$ and variance $1$. They don't look normal to me and there is no reason why standardization would yield normally distributed data.