From a technology perspective in the home broadband there are a number of providers of infrastructure - the two big ones are Openreach and Virgin. There are other players like Cityfibre, Gigaclear, B4RN, HyperOptic, etc but they tend to have smaller coverage at present.
Virgin use their own network - part fibre and part coax (some areas of the country are moving to full fibre). The coax technology that Virgin use continues to be upgraded and can in many areas provide very high speeds now (you;ll see on their website that they currently display packages up to 500Mb but the coax can go faster).
Openreach use a number of technologies as they have been gradually changing tech over the years. Many of the technologies use the copper cables that were originally installed for telephony - these include ADSL (slow by modern standards), VDSL/FTTC (quicker but limited by distance from cabinet), G.Fast (upgrade to VDSL but still dependent on distance to cabinet) and FTTP (fastest, currently have packages up to 1Gb). FTTP is only available to a small percentage of the country.
The providers you mention (TalkTalk, BT, Sky and PlusNet) all resell the Openreach services (although there are nuances as to how they do that which can make a difference to the end user experience).
Most people at present only have VDSL/FTTC available from Openreach - they are rolling out FTTP but it is going to take time.
The other providers I mention mostly have their own FTTP networks but they are limited in numbers.
You can then also add mobile networks - in slow broadband areas the mobile network may provider faster speeds that are more useful. BT own EE so provide their mobile through that network but most (or all) of the major networks now have competitively priced unlimited data packages.
Then you also have wifi networks that can provide connection via wifi rather than using cables. These tend to be very localised and somewhat sparse in availability.
There is satellite to add to the mix if you really can't get anything else but this tends to be expensive, slow and very high latency. This is a real last ditch selection at present - new satellite service might improve some of this but latency is always going to be high as it has a long way to travel.