To directly answer the question: The music teacher is friendly. I imagine Americans would say the same.
I read this and considered kindness has a level of warmth to it that friendly does not.
- friendly, helpful, well-meaning, generous, benevolent or considerate.
- warm; cordial e.g. kind regards.
- kind; behaving as a friend.
- (friendly with someone) on close or affectionate terms with them.
- relating to, or typical of, a friend.
- being a colleague, helper, partner, etc rather than an enemy
As we can see from the Chambers dictionary there is some overlap.
It has been stated that you can have one without the other, but this may be more to do with appearances.
For example if one is quiet/shy and seems distant or aloof but subtly, secretly or occasionally does really nice thoughtful things they would be said to be kind but not necessarily friendly.
Someone who is cheery and greets everyone, asks how do you do etc would at least appear very friendly but it might only be on the surface. Kindness goes deeper hence the "warmth" aspect. Someone who is kind will warm your heart. Someone who is friendly might just make you smile.
They can be used interchangeably if you really wanted but colloquially I think the difference is the depth of affection/concern/helpfulness etc.