There is a difference. Stem from = to come from. Example: her traditions stem from her culture. Rooted = embedded. Example: The roots of a flower are deeply embedded into the soil. You can also say, The flowers are deeply rooted into the soil. Or, Her traditions are deeply rooted into her culture. Meaning that whatever your talking about goes a long way back or deep into the meaning of whatever you are saying. I hope my explanation was helpful.

Both are idiomatic. To me, you could use "stem from" to describe something that is independent and distinguishable from the original source. To "be rooted in" implies that the thing you're talking about is still similar and heavily related to the original source. Does that make any sense?

As an English speaker they are more or less the same.

As an English speaker, but by no means an expert, the two phrases are more or less the same. 1. Her problems stem from her childhood. 2. Her problems are rooted in her childhood. Mean more or less the same, and I wouldn't worry about any minor differences. However, in a different sense, you can be well rooted in the ways of the world, meaning that you know the ways of the world, but you can't be well stemmed in the ways of the world!