What is an appointment with friends called?

Suppose that my wife and I talk to another couple and set a time to go to the beach with them and spend some with that couple over there. What is this arrangement and its time called? Can it be called an appointment? For example how would you say that the other couple want to postpone this arrangement and the set time?

• They called and want to postpone the appointment / rendezvous/ catch-up / arrangement / meeting.
• They cancelled the appointment / rendezvous / ... .

I know that most of these option are fine. But I don't know which ones are actually used by native speakers and will appreciate some usage examples in the case of time and place arrangements with friends.

Get-together

Or

Meetup

This would be used in Australia I can say. These words:

appointment/ rendezvous/ / arrangement / meeting

Are probably too formal to talk about a regular, but casual get together with friends.

"Date with friends" is fine. See examples of "lunch date with friends" in published books listed at Google Books.

I would use the word "gathering" no matter the size of the party.

A somewhat dated word you could use is outing, which describes an occasion when friends go "out" on the town or else beyond their regular living space to enjoy each other's company, often during activities like drinking or dancing.

The example you provide of two couples going on a casual outing together is often referred to as a double date. Typically the use of the word date on its own is reserved only to describe outings of a primarily romantic nature. However, as date means "when a couple goes on an outing", an outing attended by multiple couples can also comfortably be referred to as a date, especially as a double date (or triple date if there are three couples, etc.), regardless of how romantic the outing is.

To extend one of the comments on your question, the specific example you provide of people going to the beach together can be referred to as a beach day.

In colloquial British usage, calling the arrangement a rendezvous can be humourous because of its slightly snobbish Norman-invasion French origin while date is robustly American influenced, now trans-Atlantic. One may also use a variety of more or less illustrative activity nouns such as spree, ramble, pub-crawl, ramble,... After a proposed timing is known, one can identify it posessively as in "I won't be able to make our evening/afternoon/etc.