I'm confused because there seems to be lots of different types of power lead connectors

If you install a home charger, you will be able to ensure you have the correct connection/adaptor.  Many public charging points generally now have a selection of different connectors available.

Most new and second hand electric cars will be supplied with a lead to adapt to normal home 3-pin charging.  This is a point to check this before you purchase an EV.  If all else fails, these are widely available to buy online.