Part 2. Now for your question about whether or not the terms are interchangeable: Show versus programme? AmE : My guess is no. I don't think that AmE speakers use the word 'program (me)' in this sense. BrE: Yes, if it's light entertainment. And younger people who are more influenced by AmE may well use 'show' in the American sense, meaning that the terms might be fully interchangeable for some speakers. Series versus show/programme? Some shows/programmes are series, some are not. A one-off show is not a series, but a show that has seasons is both a show and a series. I hope that makes sense. A Venn diagram would make it clearer. One final thing to note. There is no such word as 'serie' in English. The word 'series' is both singular and plural. One series. Two series.

The definitions you have are more or less correct for British English. In BrE, the word 'show' suggests light entertainment of some kind - music, dance, games, celebrity interviews and so on. In BrE, we wouldn't normally use the word 'show' for a drama, a thriller or a documentary. For most BrE speakers, these are TV programmes, but not shows. 'TV programme' is the more general term. In other words, a TV show is a specific type of TV programme. All TV shows are TV programmes, but not all TV programmes are shows. American English differs from British English in this respect. Speakers of AmE use the word 'TV show' to cover all kinds of TV products, including dramas, thrillers and so on. I think you could probably say that the broader AmE use of 'TV show' corresponds to the BrE meaning of 'TV programme'. And yes, a series is any show (Am E or Br E) or programme (Br E) that has seasons. We all use this word in the same way. (Note that we also have the word 'serial' for a dramatised version of a story in a number of episodes. This is more of a British term, I believe.) The other thing to bear in mind is that the language is changing all the time, and Am E is becoming more and more widespread in the UK. I'm quite sure that the younger a British person is, the more likely they are to say 'TV show' rather than 'TV programme'. My prediction is that the term 'TV programme' will soon become outdated, and the Am E usage will take over.

A TV show is any televised program. It means one single showing of something on TV regardless of the content. A TV program can be substituted for show, they are the same thing. A TV series, is a set of TV shows (episodes) which are shown one after the other. Other words: A show, or program can also be called an episode.