Until December 2008 or so Przewozy Regionalne (now Polregio, then PKP Przewozy Regionalne) was a division of PKP, but due to EU rules sectors of PKP had to be broke up, so PKP Przewozy Regionalne was spun off and the shares were given to regional authorities so it became totally independent from PKP.
However only a short while after this happened, a large number of the most popular routes and the the newer (but still old) rolling stock were transferred back to PKP, which then ran many of them under the TLK brand, but some were used under other brands.
This left PR with a huge amount of those EN57/71s that all stayed with PR and other pretty old stock and mostly local routes and the occasional Intercity route under the InterRegio brand but with most of the crumbs for routes which were in most cases making huge losses.
However despite this they introduced online ticket sales in 2010, ticket machines at stations in 2011 and then the RegioEkspress brand in 2012, which offered on demand content, WIfi, plug sockets, comprehensive on-board passenger information, way before many of these were introduced by PKP - even as now WIfi is not offered on PKP's fastest trains.
Sadly RegioEkspress never really expanded after problems getting paths, issues accessing main stations in cities, steep rises to track charges and slowly died a death, buying tickets in a station was not always easy, they couldn't always install their ticket machines, PKP staff were not always keen to sell their tickets and also in some cases, some station timetables didn't even list them - the companies precarious finances worsened and services got cut more to the point where everything other than standard regio services were cut.
PolRegio is basically the new PR, which now is managed by the Industrial Development Agency in Poland which bought it's shares, many of the regions who owned shares in PR have in the last number of years set up their own railway companies which have since took over routes and also in a number of cases stock that was previously operated by PR which was bought by the regions.
The end result is pretty much that the parts of PR with newer trains have been assumed into these new regional companies and are operating under the new providers names, whilst the stuff that has been left continues to run on the older trains under the PolRegio name.
This was one of the RegioEkspress trains - this one was refurbished to RE standards in 2012 - (click the CC icon in the video for English subtitles)
The above is why I would admire PR a lot - they had little money and always have had a bad hand - but when those trains were first introduced they were WAY ahead of anything PKP could offer and that's before you take into account the fact they also had ticket machines and online sales way before PKP as well.
The real tragedy about PKP is they have had huge amount of taxpayers money for the past decade, and still cannot get the basics right, they could be a vastly better railway company than they are with their resources.