You're probably well aware of the expression "don't judge a book by its cover." It means that you shouldn't decide whether you like something before you try it. This same philosophy also applies to the job search.
What I mean is you shouldn't completely dismiss a job based on its title. A lot of job seekers are often put off or intimidated by the names of the positions they find online. Words like "senior" or "assistant" can paint preconceived notions of what the work will be like, and whether they are qualified. The first instinct in these instances would be to not waste any time and move on to the next position. This would be a mistake.
Just as you wouldn't judge a book by its cover you also shouldn't judge a job by its title. Before deciding you are too good/not good enough for the employment, take a look at the job description. The names given to positions are not always indicative of seniority. For example, HR policies can dictate that less impressive titles are not doled as often, leaving pretty important jobs with less than important names.
At the end of the day, the words at the top of the wanted aren't what is important -- it's the work you will be doing that matters.