Are Keys with minor or major pentatonic and minor harmonic scales named differently or how do you discern the scale based on the key if it's pentatonic or harmonic instead of natural?
The key is more about the tonic than any scale. A key is not pentatonic or natural or Dorian or harmonic or melodic. A key tells you two things: (1) a note name giving the home note i.e. tonic, and (2) the type of the home chord i.e. tonic chord, is it major or minor. The major/minor thing does not mean a list of "allowed" notes, it means the harmony around the home note.
Since the tonic chord already specifies the tonic note, we can simplify the formula of key as:
- KEY = TONIC CHORD
... and accordingly, the name of the key follows the name of a basic chord. "This song is in A minor." A minor, the chord, not A minor, the scale.
When you're told that a song is in a key, it is to let you know what the prominent home note is, and whether the home chord is a major or minor chord. A wide variety of different scales and harmonies may be used, and the harmony may be almost anything during the song, changing and mixing harmonic feelings from different scales back and forth, but as long as the home chord stays the same, it will be in the same key.
However, you can assume a default reference scale based on the key. The reference scale is the notes you get from the key's key signature. For example if a song is said to be "in A minor", then you can assume the A minor natural scale as a basic reference grid to which you relate the song's actual harmony. For example if there's an A major chord somewhere in the song, you'll note that as a somewhat remarkable point, because an accidental is needed for writing the C# note.
This has been asked countless times, and new askers keep appearing endlessly. I think the difficulty of understanding the concept of key comes from the tonic being "invisible". You have to feel the tonic, i.e. when the melody feels to be at home. You have to actually hear the music.