The examples you give result in two very different ideas, so there is no one word for them all. There is however a word that describes each.
For your first two examples, you'll use the term relative to describe the scales as they contain the exact same notes, but the pattern used to create them is different. For example, A minor is the relative minor of C major. Typically this is only used for major and minor, but the idea can be extended to modes. Another option would be in this scenario would be to call it a mode of the parent scale. For example, D dorian is a mode of C major.
The last one is different as the information isn't really useful to convey because every scale has this relationship with the chromatic scale. Therefore the term used to describe it is subset as it only has some of the notes of the scale. For example, C major pentatonic is a subset of C major. The reason why this isn't really the most important relationship can be seen in your example of C major petnatonic. There are 4 other seven note scales that have the same 5 notes including C major, C Lydian, C Mixolydian, and C Lydian Dominant. So while yes it has a lot of overlap with C Major, it shares the same overlap with 3 other scales which is why we view the major petnatonic scale as different from just the major scale.