fwiw this isn't the definition I've ever used. In any company I've developed software for, you just described a closed beta. An open beta is literally open to everyone (or to all existing clients) with the provisio that they understand its a beta.The difference between an "Open Beta" and a "Public Release" is that an open beta is a brief time period (weekend, week, fortnight, ???) where the software is available to a larger group before being shut down again while the issues found are corrected.
(And a "public release" is literally "going to production")
Naturally, ymmv. Maybe Canada's just weird