How do international bank-to-bank transfers function end to end?

Its simply a ledger adjustment. All banks report to the central banks and central banks exchange ledger positions with each other.

So, when money needs to from UK to say Philippines, its simply a debit on one side and credit on the other (though I am putting this in a very very simplistic way).

Another easy way to picture this, is to imagine a classroom. Each classroom has many students and one teacher.

Each student = bank
Teacher = central bank.

Now imagine each student (bank) has a ledger in front of them. Anything they write, others can see, and more specifically the teacher (central bank) also writes down in its ledger.

For any student (bank) to cheat, all other students (banks) will know and there would be a discrepancy between the cheating student (bank)'s ledger and the teacher (central bank)'s ledger position.

For cross-border to occur, imagine all the teacher (central banks) now sitting in one class and exchanging their ledger positions.

All this is done electronically.

The cash is physical movement and for that, yes, planes are used and cash is transported via the aircraft.