Employee/employer relationship is normally more formalised with contracts and wages. This is to ensure that the employer isn't taking advantage of loopholes.
Chances are you will get classed as a "disguised employee" if you are freelance and invoicing only 1 client.
But I don't know employment law where you are. I know the US and UK have laws about this, chances are EU does as well.
Ye though it's more complex when you are from EU and want to work for US company. Also for now it's more like part time job hope to get full contract one next year :)