I know it's an old post, but anyway.
The song that consists of two songs is just a Medley, where one song continues into the next. The others are more interesting because they do the changes for different reasons, usually to change the mood.
Folk music is Modal, which is different from classical music etc. which is Tonal.
Modal music is based on scales and Tonal music is based on chord progressions, roughly speaking. They're completely different ways of approaching music theory.
Both kinds can change from one scale to another, but in tonal music it will usually happen gradually and by leading the melodies through fluid modulations from one scale to the next, so that the change is expected by the listener before it happens.
Modal music doesn't have as many criteria for what is right or wrong and can therefore make more abrupt changes which will sound more surprising. I'm not sure the transition has any specific name. It's just a change of mode.
In modern music this can also be achieved by mixing tonality and modality. This is called Modal Interchange and technically follows the strict theory while also making use of modal scales. The general idea is to map out all the notes that are "restricted" by the chords following conventional rules and then using all the undefined notes to "legally" play out of the expected scale. Being able to do this on the fly is key to good improvisation, but it can also be used as a basis for entire songs, as in progressive rock/jazz.