Yes indeed Joe, you can sing them in public freely, the venue pays a fee to PRS. You may be asked to fill in a form by the venue to be sent to PRS.
If you record them you pay MCPS for use, they give you the permission for use on behalf of [*who they think is] the copyright holder, who is paid by them less their percentage.
*Lots of stories about who has claimed what copyright for which song over the years! E.g. a famous collector paying some cash and saying the singer recorded/collected from could now only sing the song in public for x years under certain conditions.
It is the same in Scotland / Wales / N. Ireland / England.
Different in the USA. I have been paid lump sums direct from singers for permissions to record.