from a helpful volunteer in this talk page, we have a brief description of some frequently used terms such as ER & O.
"ER" = Engineering Run, "O" = Observing Run.
One crucial distinction is that astronomically meaningful observations require not only the interferometers to be locked in their nominal low noise state for as long as possible at a time, and working in concert; they also depend on them being accurately calibrated. I.e. it must be known by how much the measured quantities change for a given (tiny) displacement of the test masses. While the Detector Characterization team has kept working to mitigate noise sources throughout the observing runs, any changes that would affect the calibration can only be made between observing runs. Within each run, it is carefully kept constant.
(O3b having been cut short by a month due to Covid-19 measures; O3a and O3b together comprise O3)
The O4 Observing run started on 24 May 2023. The first period of the O4 observing run, O4a, ended at 16:00 UTC on 16 January 2024 for installation and maintenance activities. The second period of O4, O4b, started 10 April 2024 and is currently ongoing, with a planned end date of 9 June 2025.