Do you find labels for your interaction with your polycule helpful, or limiting? I know some folks find it much easier to have conversations about the kinds of interactions they want to have with metamours, for example, if they start from a basis of "I like the idea of kitchen table polyamory - for me that means [ insert here]. How do you feel about that?" Other people find that starting from the terms predisposes people to certain reactions and they don't like those reactions - they'd rather go from activities or situations as a basis for their boundaries and interactions. Some people have had bad experiences with a particular term in a past relationship and react strongly as a result - I know a few people who thanks to past coerced kitchen table situations approach with a lot of caution people who make kitchen table a requirement rather than a preference; and others who fear what limits a parallel polyamory situation might put on their relationship.
All of these are valid concerns, but the best way to avoid any of the bad sides of them is to talk out actual situations and particular concerns. If you're worried that being parallel will limit your time with your partner because they nest with another partner - ask how they handle those logistics/what the schedule is like/whether parallel means never being in the same room or just not doing activities together. If you're concerned that kitchen table might get limiting or coercive, ask about what happens if you don't get along with other polycule members, or if schedules end up less compatible and you end up missing bigger polycule events. Make sure that your definitions of kitchen table are similar - if one person means "a monthly board game night and potluck" and the other means "twice a week group hangouts and ideally you'll also become romantically or sexually involved with at least one other polycule member" you might not be compatible.
Some of the newer labels mean to disambiguate this - lap-sitting polyamory to indicate kitchen table with some additional expectations that might involve physical closeness, for example - but because none of these are in any way standardized, and because no two relationships are the same, instead I find that in real life, these just add to the confusion. My advice remains the same as it's ever been - identify your boundaries, communicate and enforce them as consistently as you can, and if your partners and metas do the same, the label or lack thereof doesn't matter.
If you want to discuss and learn more about various kinds of polycule interrelationship, come to Beyond The Kitchen Table this Sunday, January 23 at 3 pm Eastern. Tickets are available for just this class or as a two-class bundle with my Relationship Anarchy class in February, both here. You can also get more information on this in my book, available in paperback, eBook and on Kindle Unlimited here. If you don't follow me on my social media, you might not have heard me screaming like a fangirl yesterday - Dan Savage mentioned my site yesterday on the Savage Lovecast at about minute 49 while defining kitchen table polyamory and I lost it over that.