I think when you talk about cores, you're talking about the guys you want to stick with and build a team around for the forseeable future. It's usually the elite players that are on a team's roster.
That kind of evolves as some of the older core get older and get moved out as a young core emerges.
I want the team to build around Swayman, McAvoy, and Pasta. To me, that's the main core and everyone else, while good players that add value to the team, aren't elite and can be moved for the right price ( not that I'm advocating for it ).
I agree with your definition here. I think the term gets overused or thrown around too much to where it starts to lose meaning. Your core of Swayman, Mac, and Pasta sounds about right, and on the current roster, obviously Brad. Those are four players you keep come hell or high water and build around. Brad will have 2-3 years left in him, most likely, and there may be a young player that really emerges to become core: a player like Frederic, perhaps (not saying he will, just that idea). The rest of the regulars, like Carlo, Lindholm, Ullmark, who are good players for us are guys you can move for the right deal, they price themselves beyond their skillsets, or when/if you have a better option available. Jake falls into that category.