In the UK, there is a difference between a TV show and a TV programme.
'TV show' usually refers to a particular type of light entertainment product - a show often has a celebrity host or hosts, and may involve any combination of interviews, music and comedy.
'TV programme' covers a wider range of broadcasts, including more serious ones. The term 'programme' covers broadcasts which are not 'shows' - for example, reportage, documentaries and dramas.
In short, all shows are programmes, but not all programmes are shows.