Yes and I'm not the only one. There perhaps was a relatively established meaning in the US which some prominent personalities are trying to pile into, but in the UK, it is far more complicated.
Any more members' perspectives about what we are / shall be "reforming from" and the slogan "reformanda" with an -a on the end, would be welcome, please.
For example there are:
- organisational ties (this seems to be the main thing now in the UK: the term they apply is "positioning")
- ceremonial proceedings which maybe wouldn't mean much to some attending
- actual belief and meanings of belief
- varying points of dogma
(I only put this in "Calvinist / Presbyterian" because almost all churches are "reformed".)
("Non denominational" is not my choice of self description, when I last looked the list didn't have "multi-denominational".)
"Reformed" though (as applied to this forum) entails a certain set of doctrines; (which I'm assuming you know that). That's a different context than a church (or other organization) "reforming" (for example) their statement of faith / statement of purpose to "keep up with the times".
Now if "reforming churches" (i.e. "keep up with the times") is what your referring to as happening in the UK; and it's not related to what's commonly called "calvinism" doctrinally? That would be a different question altogether.
In general though; there has been a trend also in the US of "evangelical" churches moving more toward "calvinistic" doctrine. (And tell me if I'm wrong here; but that I think is the question you're really asking?)
So if the questions leading off of that are:
"Is there a distinction between evangelical / doctrinally calvinistic churches and traditional doctrinally calvinistic churches?"
My experience over the past 30 years would say "yes". "Evangelical calvinistic" churches tend to be closer in "evangelical behavioral practices" to (conservative) "arminian evangelical churches" (like typical "run of the mill" baptist churches) than they are to "traditionally calvinistic" churches.
And churches that are more "evangelically lively" tend to be (at least what people in the US would refer to as) "Spirit filled". On the flip side of that question though; for conservative evangelicals (be they "arminian" or "calvinistic") "spirit-filled" tends to evoke notions of pentecostalism. I don't know if that's the same in the UK or not? In the US though; depending on "conservative" or "liberal"; "spirit filled" tends to evoke images of pentecostalism. And if the evangelical is more "conservative" they'll see that as negative. If they are more "liberal" they'll see that as positive.
And in that mix (which as a British person you might find this odd about American churches); you will see some convergence between political "conservative / liberal" that trends into those diverging circles. America right now is very politically divided; which also manifests with ideological social divisions too.
So (as I'm sure you are aware of this too); just as "evangelical" carries its own stereotypes; so does "reformed", "calvinistic", "conservative" and "liberal".
Now as for your question of things like "organizational ties"?
You will see some "narrowing of parameters" in certain denominations. For example; the Orthodox Presbyterian Church (OPC) in America tends to be a very "traditional reformed" / "non-evangelical" "calvinistic" denomination. A church of common tenant in Europe might be the Dutch Reformed Church. (There's a lot of Dutch Reformed people in the OPC in the US.)
Practice wise; the OPC church would be the most "puritan". They sing songs, read Bible, have prayers, sermon, communion (usually once a month) and that's it. It's a very basic and predictable service; but not liturgical like C of E, or Lutherans would be.
Eschatology wise; OPC tends to be amillennial / partial-Preterist; whereas arminian evangelicals tend to be premillennial dispensationalists.
The OPC also tends to be very historical document / catechism orientated. Much of the seminary learning of the preachers comes out of that historical background. Also the OPC does not have female preachers or elders; but may have female "deacons" in the sense of administrative type church work (treasurer / building upkeep / community use committees. Churches in the US do rent out their buildings to non-church civic organizations; like 12 step groups, scouts groups, or day care centers.
Whereas the Presbyterian Church in America (PCA) (which had been 25 or more years ago; much more like the OPC in belief and religious practice); now tends to be more "arminian" / socially / politically "liberal" in practice. Despite the fact that the profession of faith may be very historically aligned to the documents that came out of the Reformation.
America also has quite a few "community churches" that can run the gambit of "evangelical", "Calvinistic doctrine" "conservative", or closer to "pentecostal" etc. There's a real mixed bag in that category.
Now in America; the more "evangelical" / "arminian" / "pentecostal" leaning a church gets; the more "contemporary Christian" the music tends to become. Those churches also can get quite large. But also "evangelical" / "arminian" / "non-pentecostal" churches can be quite large too. Sometimes large churches are called "mainstream churches"; which tends to be an adjective related to size. (Usually 500 or more people there every Sunday.) If one gets 2000 or more attendees; than they earn the title "mega church".
Rarely does a "calvinistic" church get that big; but there are some. John McArther Grace Community Church has 8,000 weekly average attendance. Music wise though, I think that church is pretty much still hymn type music.
Now "dogma"? Differences there tend to ebb and flow with what ever is "trending" in those circles. I remember maybe 10 or more years ago there was a trend "headship doctrine" that was going around conservative "doctrinally calvinistic" churches. Things like that though tend to eventually cause "break offs" into what usually becomes some sort of "independent reformed baptist" type church.
My experience with those is that they tend to be so "reductionist" that they don't tend to last long. Some small groups like that though do function well. I was once in a "house church" that was very supportive. There were maybe 4 couples and a couple of single people who were part of that group. It only lasted for a couple of years though because the guy who was serving as the "pastor" worked for a defense contractor and they got moved to another state. But that's happened with a lot of smaller groups I've been in; (even attached to established churches). People move, then you loose track of each other. It can be hard; but it happens.
So, I don't know if I answered your questions; but? That's kind of my "stab in the dark" as far as what I think you might be asking.