First of all from a linguistic view: "permit" means having right to do something and residency means current place of your stay.
Generally, when we are relocating to another country (Lets say country A), we are getting "Resident Permit" from immigration office of Country A. By using that document we are entering Country A and then going to a local authority to register ourselves as residents.
So, I assume having resident permit does not mean that your residency changed until you register to the local authorities.
This relates to following practical situation:
My family and I living in Finland under EU Blue Card. I got a job offer from Germany and planning to apply for German EU Blue Card. But my new employer wants me to relocate to Germany 2 months later since their new office is not ready and the first two months are for on-boarding training.
So I wonder when we apply for a new Blue card, do we lose our rights gained from our current EU Blue cards. I mean like health insurances, kindergarden services etc.
I know that Finnish EU Blue Card provides an extra 3 months when you resign your job to let you find a new job.