My question is about what should be go first in software developing: database model or domain model? Or these notion are parallels? Thanks.
It depends on whether you're a database or an object person. Each one would claim supremacy and say that their specialty should be done first.
I'd disagree with both. The first thing you should do is understand your problem well. The model and schema will flow from that.
You can't get rid of the object-relational mismatch impedence, no matter what you do. Objects are instance-based; SQL is set-based. You'll still have the problem.