The general rule both in the the UK and the United States is to pass "port to port", i.e. on the right on the oncoming vessel (so each vessel has the other on its port side). However, passing starboard to starboard is OK if necessary, provided signals are given and acknowledged.

Anyway, in the UK sailors refer to passing "wrong side":

"The Rule of the Road
Port to port - Whilst the general rule is pass ’port to port’ (i.e. to the right), there may be situations where it is safer not to do this - eg passing in a lock pound when one boat has got seriously out of position, where the lock or bridge is at a difficult angle, or where one boat is preparing to moor.
Watch out for situations to pass ‘wrong side’ and indicate your intention by using the recognised sound signal (two blasts on the horn)."
https://www.waterways.org.uk/boating/navigating_your_boat/ca...

Here they are discussing the fact that in Germany boats "drive on the left", passing starboard to starboard:

"OK so sitting by the Rhine this evening, why do the boats "drive on the left" I thought we drove on the right because of ColRegs and that would apply everywhere, but apparently not!
is it a depth thing?"
I don't think so as they are big barges and are passing "wrong"side so there must be depth"
https://canalworld.net/forums/index.php?/topic/56169-rhine-b...

I'm not sure whether this is said in the US, though. Perhaps "on the wrong side" would be better there:

"There were lengthy delays for drawbridges (39 bridges between Lantana and Miami) and small boats were constantly trying to pass on the wrong side."
http://boatbugout.blogspot.com.es/