I'm
just wondering if my conception of what is a cross country
flight is correct.

There's no such concept as "correct" in this case. It would imply that there's only one way (or one set of ways) to look at any particular leg.

Somebody upthread mused that ones entire flight career could be considered one long cross country, and "surely the FAA didn't have this in mind". Well, to my knowledge it hasn't been tested in court, but (absent a clever use of careless and
reckless) it is not against the rules. It's also not unimaginably unreasonable either.

For me, if I take off for a place a
thousand miles away, every bit of the long trip is XC,
requiring navigation, pilotage, and all the skills. It does
not matter if I only fly 25 miles some days, and 300 miles
on other days or split it up as 150 miles the first day and
175 the second. It's all part of the same long XC.

If that's how you view it, then that's how you log it. You count the time.

You see, logging is an imperfect art, and hours in a logbook do not equate well to "experience gained". Imperfections (or imprecision) in whether a particular hour was cross country pale in comparison to the difference between flying 100 hours, and
flying the same hour 100 times, as it relates to how much "better" a pilot one is afterwards, and the point of a logbook (to the FAA) is to measure, in some way, pilot experience (and to infer quality, albeit imperfectly) for the purpose of flight
privelages (or rights, I won't get into that here

The same kind of issue comes up when logging "actual" (IFR) time. Just how soupy does it need to be? And what if you are "in and out"?

Here's one rule I use for IFR time: If I enter a cloud at any point in the flight, then the flight gets at least .1 actual in the logbook, even if I was only in for five seconds. It's my way of noting that I was in fact in cloud that flight. I try
to compensate by not logging .2 or more unless I'm clearly past .2, but it doesn't really matter because there are so many other vaguearies involved.

So, break your trip (what's a "trip"?) into as many or as few legs as you like, and log what feels right to you as XC or as local. If you do this, you'll have some reasoning behind whatever you log, and I think that's all the FAA is after.

(is it cross country if you land at the same airport, but a different runway? Suppose it's a really big airport?

Jose