Hi monoj mon,
Just a few articles further (33), there would have been your answer:
Eudamed consists of 7 electronic systems
(a) the electronic system for registration of devices referred to in Article 29(4);
(b) the UDI-database referred to in Article 28;
(c) the electronic system on registration of economic operators referred to in Article 30;
(d) the electronic system on notified bodies and on certificates referred to in Article 57;
(e) the electronic system on clinical investigations referred to in Article 73;
(f) the electronic system on vigilance and post-market surveillance referred to in Article 92;
(g) the electronic system on market surveillance referred to in Article 100.
So the UDI-database is part of Eudamed
But if your real question was, if there were different systems for UDI and device registration, the answer is yes.