In terms of crude overall numbers, private railway companies tend to open stations whilst nationalised networks have a history of closing them.
That's not right in any relevant sense ..
Pre-1948, (largely - I'll exclude random things like military railways..) only private railway companies existed. They therefore opened stations because stations didn't exist, and if you were building a railway with neither stations nor goods depots, you wouldn't have a railway you would have 'tracks'..
Between 1994 and 2025, which railway stations have the private sector opened?
Railtrack did some - but find one that private sector actually funded?
After them.. Network Rail is a government owned body - it owns and builds stations, except where another government or public sector body such as a council, have funded or directly built it (such as Ebbw Vale reopening). I'm struggling to think of a single station opened by the private sector - perhaps a shopping centre (oh, no, didn't quite get White Rose opened.. council money ran out to link up the private shopping centre)., or perhaps HS1 Ebbsfleet - but that was government backed too.
If there was a station opened by the private sector, it's perhaps something Chiltern... they did some big work funded privately on Chiltern Mainline/Evergreen project to redouble to Banbury from Princes Risborough.