Embroidery thread for machines just means that it's usually shinier and a bit thicker than normal sewing thread, usually a bit stronger because of that. I can't imagine that the brands would make too much of a difference to your machine, I'd be more worried about using a new needle with the right sized hole, and also the right one for the material you're embroidering.

Obivously, companies that make thread and sewing machines want to promote brand loyalty, so they ONLY recommend their own stuff to match their machine, but I've never had any issues before.