There are over a 150 legal entities in the BT Group around the world. BT purchased Plusnet some years ago with probably the intention of gaining customers and amalgamating the company. However Plusnet continues to thrive as a successful business with consistent top awards for their customer service. Therefore it continues to be branded and run separately from BT.
Separate branding is to ensure people do not get confused between BT Consumer and Plusnet product offerings. Thats just like many of the clothing shops in the high street that all belong to the same group.
Being part of BT has its advantages as Plusnet shares some of the core BT network and BT's exclusive connectivity to things like BBC iPlayer and Netflix. So if you want the best service without the monolithic BT offering you can't go far wrong.
Please note that any of the providers that offer "up to" broadband are using the Openreach infrastructure (also BT). They provide to the ISPs including BT and Plusnet in a neutral way with the same cost and service regardless of who the ISP is. The ISPs then add their own network topology to access the Internet (investment varies) and their add-ons. So the service provided by Openreach is the same. You either live near your exchange (ADSL) or cabinet (FTTC) or you don't, you either have a good copper pair or you don't. That determines the speed and changing ISP provider makes little difference. The only difference is the ISPs bandwidth from the exchange to the Internet, the quality of their router, the add-on services and how much they charge. Look carefully at the add-ons, if they are of benefit to you, then a slightly higher broadband cost may save you money elsewhere. People initially look at the BT price as high but not if you time your contract right and you utilise the whole package.
Where people claim a boost in speed its either because they have moved from ADSL to FTTC or the change of ISP Router reset their home network and devices.
The only way to get a different broadband service at your location is to pay extra and get a new install with a new ISP then a recovery of the old to get a new copper pair however this may end being worse. Alternatively move to a provider that has their own infrastructure like Virgin Media.
Remember a fast line speed does not equal fast Internet. I had a 200Mbps Virgin service during 2017 but the TV still buffered at 8.00pm on a Saturday.