Yes, senior is mid-level if you look at a ladder. It's usually SWE I, SWE II, Senior, Staff, Senior Staff, Principal, Distinguished, etc. for large companies.

What I meant was that large companies expect all hires to eventually hit senior, give or take 3 - 6 years. If you don't, they have something of an "up or out" approach, where it counts against you in subsequent reviews. However, not everyone is expected to achieve Staff or higher.