I don't know if the original post was a typo or if the intent was to refer to an actual place that I don't know about. (I seriously don't know - I'm not being cheeky.) To be clear, it is "Salish Sea" ... around here. I don't think there is a "Sailish Sea", but maybe there is, somewhere?
As for whether it will always be “Puget Sound” for many people - Puget Sound is only a part (maybe 1/3) of the Salish Sea. And, up here (north of the Strait of Juan de Fuca), I don’t know anyone who considers this area part of Puget Sound except maybe in a fairly loose or colloquial sense. Sometimes it’s called “Northern Puget Sound,” but that’s only Puget Sound in the way Northern Ireland is Ireland - at least as folks around here see it. Our region (the San Juan and Gulf Islands) is viewed as distinct from Puget Sound, even though everyone recognizes it’s part of some larger (previously unnamed) system.
That said, if you referred to the whole area as “Puget Sound,” it wouldn’t exactly cause confusion. People would likely get what you meant from context. And, most people wouldn't correct you. Still, no one I know uses "Puget Sound" to refer to the waters north of the Canadian border and doing so would result in confusion - whereas they fit naturally into the concept of the Salish Sea.
Prior to the adoption of the term “Salish Sea,” there was no single widely accepted name for the entire inland sea stretching from around Discovery Passage to the southern tip of Puget Sound. The geography was clear, but the language was not.
I grew up in Washington and we learned about the region in school (about 40+ years ago). The term "Salish Sea" was not in use, then, but we did learn that Puget Sound was south of the Strait of Juan de Fuca. I remember this being on a test and one of the choices, with the San Juans being part of Puget Sound, was distinctly the wrong answer.
I’ve been surprised that a handful of people resist the term “Salish Sea,” as if it were replacing something they preferred - when, in fact, it isn’t.