It depends on what they've been invited to. Neither of those are standard callings - at least not with that exact phraseology.
As for the meetings, I assume you're talking about "Stake Priesthood Executive Committee Meeting (High Council Meeting)" described in Handbook 2: 18.3.6 which "meets twice monthly, where feasible" and the Stake Council Meeting described in Handbook 2: 18.3.7 which "meets two to four times a year as needed". Both of those say "The stake presidency may invite others to attend as needed."
I've been a STS for ages and have never been a part of a regular series of meetings, so I can't say. If there's a problem or a need, either the stake clerk or executive secretary lets me know about it.
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