I'm not huge on the labels. I think calling someone a junior or a senior is a good way to falsely categorize the office and weight opinions where they need not be weighted. There can also be some flaring of egos for no good reason. Having said that, there are plenty of places who use the junior/senior tags well but not all of them do. We recently got a 'Senior Project Analyst', the qualifications? 23 years seniority, most of which was spent elsewhere. He hates the label too but this is what the company gave him. Absent from my email signature is the demarcation despite having spent over 5 years in supply chain related software development and going on 9 with the company so far.
I recently listened to a hanselminutes podcast, that had a ton of information in it about what you're asking. I would give it a listen.
I would say look carefully at the qualifications being asked for in the posting. If you can speak and work effectively through them just apply. The company knows what it's looking for and if you don't cut it for them with 0 years or 10 years they'll let you know.