Blahagun

I have 18 years of professional experience with developing software. I have been employed with six companies through these years and had a three year stint working on my own company. I recently applied for a job, where they offered me a developer position, although they had an opening for a senior developer position. What exactly are most companies looking for a senior position? Is it mostly the way you sell yourself? Because even with my years of experience I have never put a label on myself as a "senior". I always thought that this is implied.