The naming of the notes isn't always consistent. The major scale is fairly easy. There are seven (different) diatonic notes; the other five tones from the chromatic scale are called "chromatic" to distinguish them from diatonic notes. There are actually 21 named notes (each note, its sharp, and its flat) for a total of 12 different notes.
In the minor mode, things are not as well described. There are still seven note names, but.....there are two "mutable" notes. The "natural" form of the minor scale has seven notes but compared to the major scale, notes 3, 6, and 7 are a half step lower. To get a half step close from note 7, the 7th note can be raised (gives a major V chord too); then to avoid (for singers) the augmented 2nd between note 6 and raised note 7, note 6 is raised. Neither of these moves is treated as chromatic in general.
If one keeps seven note name and writes out the 4 different scales that occur when sorting the notes by pitch, one gets four forms of minor scale. The "natural" minor is just 1,2,3,4,5,6,7; the "harmonic" minor is 1,2,3,4,5,6,#7; the "melodic minor" is 1,2,3,4,5,#6,#7 ascending and 1,2,3,4,5,6,7 descending. There doesn't seem to be a common name for 1,2,3,4,5,#6,7 but that doesn't mean there are not occurrences of this pattern.
From a Common Practice Period harmonic point of view ("classical harmonic") there are only two modes: the major and the minor (which has mutable notes.) In classical theory, scales are just the result of sorting notes by pitch so the minor mode is usually thought of as the "natural" minor scale with two mutable notes rather than three separate entities. There are lots of classical pieces with all three forms of scale occurring the same passage. I don't know enough about jazz and popular harmonic descriptions to go into to discuss much of their usage.
There are a few tendencies used in classical music related to mutable notes; these are only tendencies and other practices are not uncommon.
When the underlying harmony of a passage is tonic, tones 6 and 7 are often raised in ascending passages and lowered in descending passages. This gives rise to the "melodic" minor. However, often the 6 is kept lowered and the7 raised in instrumental music.
When the underlying harmony is subdominant, the "natural" form is used for both ascending and descending scale passages (the lowered 6 is the third of the iv chord.) Again this rule is sometime broken.
When the underlying harmony is dominant, the raised form is often used in both ascending and descending passages. Again the "harmonic" minor occurs too. The flat 7 forms a ninth chord with dominant harmony.
The arpeggio on a dominant chord is common which leads to the raised second between the lowered 6 and raised 7 steps. (2,4,5,b6,7 is a dominant ninth in third inversion.)