You can read the guide in my signature for a more in depth explanation and guide on how to use sim-c and AMR to optimize your character. But here is a basic explanation.
They are both the same thing. However, normalized is simply, well, a normalized weight where strength always equals 1. This is also known as SEP, or strength equivalence point. Normalized is generally used for a "quick glance" where you can see how well stats scale in relation to strength, and also for napkin math, if you want to compare two pieces of gear. Just multiply the secondary stats by their normalized value and add them. Whichever piece has the higher number is better, assuming equal strength and equal stat weights.
Lets say you sim, and you get a result of "str is 4.32, haste is 3.24, crit is 0.33" etc. These are the values of "virtual dps" that these stats give you - i.e. 1 point of str will give you 4.32 "virtual dps", etc.
Normalized means it takes one stat (str, for example) and gives it a value of 1. So if your stats are normalized around str, then 1 point in str gives you 1 "virtual dps" point.
So normalized statline can look like this:
str: 1, crit: 0.48, haste: 2.34 etc.
This means that (if you assume that str gives you 1 point), crit will give you 0.48 points etc.
So the difference between normalized and non-normalized is whether you want to know actual numbers or their relation. Both are useful for different cases.
-If you're comparing pieces of gear, normalized is usually easier to use to see which is better
-If you're doing reforging or math calculations, non-normalized might be useful depending on what you do