Learn English – word for “hard camping”

First, that description of "been to" and "gone to" is mostly accurate. However, to "have gone to" a place can mean that you're no longer there, the same as if you "have been to" a place. (There are other subtle differences between these two expressions; see the previous edit to see them.)

It seems to me that the same logic doesn't quite apply for "have been on a trip"/"have gone on a trip". The latter two are mostly interchangeable, although there might be slightly different nuances about the "default" interpretation. I'll quickly go through some examples.

Both of the "on a trip" expressions can be used to mean you're still on that trip:

(1) I've been on a trip to Europe these past six months.
_{The speaker is still in Europe.}

(2) I've gone on a trip to Europe and I won't be back till August.
_{The speaker is still in Europe.}

And both of them can mean that you are not still on that trip (helped by including the word "ever"):

(3) Have you ever been on a trip to Europe?
_{The speaker is no longer in Europe.}

(4) Have you ever gone on a trip to Europe?
_{The speaker is no longer in Europe.}

So the two expressions pattern like "been to" and "gone to" except that "been to" would not work where "been on a trip to" works in sentence (1):

(1b) ✗? I've been to Europe these past six months.
_{If this works at all, it means the speaker went in the past six months and is no longer in Europe.}

Since both meanings are possible, what's the default interpretation without context?

In British English, I'd say it's the same as "been to" and "gone to". In North American English, I would say it's the reverse. (This is based on my and my relatives' usage. I am AmE and my relatives BrE.)

(5) I've been on a trip to Europe.
_{BrE: The speaker is probably back. AmE: The speaker is probably still there.}

(6) I've gone on a trip to Europe.
_{BrE: The speaker is probably still there. AmE: The speaker is probably back.}

To generalize a bit, I imagine that both the above pattern and the account you cited in your question owe a lot to the fact that in British English, "to have been" is often used in the sense that NA English uses the simple past.

— "Was there anything in the mailbox?"
— "I've just been. There wasn't anything." (BrE)
— "I just went. There wasn't anything." (AmE)

Even two phrases that appear identical can mean two different things depending on the region.

"I've been swimming today."
usually means "I went swimming earlier today." (BrE)
usually means "I was swimming earlier today." (AmE)

P.S. Another minor difference between "been to"/"gone to" and "been on a trip"/"gone on a trip" is that the "been" in "been on a trip" can be conjugated in any tense:

✓ Next week I'll be on a trip to Europe.
_{✗ Next week I'll be to Europe.}

✓ Right now I am on a trip to Europe.
_{✗ Right now I am to Europe.}

There is a cooking terminology difference between the two, yes, particularly in the US. If something is "minced" the implication is that it's chopped very finely with a knife or blade, either manually or with a machine like a food processor. It's much less common to use the term "mince" in the US to refer to meat that has been put through a grinder, which is referred to as "ground". Grinding is a combination of pressing, cutting, and extruding to achieve a relatively uniform result.

I generally do not see the term "minced" used to refer to "ground" meat in the US at all (in the UK, "minced" is the standard term).

"Ground" is used for all sorts of products put through a grinder.

As noted, "ground" does not refer to the land in this case (note that "you're grounded" actually does refer to the land as it comes from the aviation-related terminology of being prohibited from flying). It is an adjectival usage of the past tense of "grind". The dictionary linked here includes the definition:

b) American English to cut food, especially raw meat, into very small pieces by putting it through a machine SYN mince British English