The 7 modes derived from the Major scale system are named after early Greek tribes [the Ionians, the Lydians, etc.]. Modes have become almost mythic in their status. There is no proof that the Dorians used only the Dorian mode, or that the Phrygians only used the Phrygian, etc.
The Major scale has 7 tones, & all of them can be a ‘starting point’ for a scale. Yet, ‘starting points’ are just a concept. We don’t have to ‘start’ on a particular tone to produce the modal flavors. This is because the underlying harmony determines how melodic tones are perceived, unless there isn't harmony present. Though at the same time, we can use modes over chords which do not share the same root (we can "substitute", as modes are transportable).
The basic rule for scales is that the number of tones in the scale is the minimum number of names that it can have [some modes have more than one name; C Major is also called C Ionian!]. Every tone in the scale can be a root [or 1] for a scale. Since the Major Scale has 7 tones, there are 7 scales within the tone group. This is called 'derivative'. Again, every tone in the scale can be a ‘starting point’ [root]. When we play ‘tone to tone’ [e.g. D to D] in a particular key, we are playing in a new mode. We can also create modes by 'paralleling'. This means that we compare what's different in a mode to the Major scale (we modify the Major to create modes; and to do this, we use formulas...♯4, ♭5, etc.).
Note: there are 21 modes created from the Major scale group, the Harmonic minor, & the Melodic minor. The 7 basic mode names found in the Major key are used to describe further modifications found in the minor scale groups. When we get into Harmonic minor territory, we hear "Ionian ♯5". This means everything as is, in the Major scale, but with one modification...the ♯5. We hear all of the mode names again, in some form.
What this means is that each mode type in the Major has a tone or set of tones which describe them. Example: Lydian is a Major scale with a ♯4. This combination: Major 3rd with a ♯4 is what defines Lydian. So when we hear "Lydian Dominant", this means, Major scale with a #4 that is also Dominant [Dominant = Major with a ♭7 - it would be strange to say "Lydian Mixolydian" but this is 'correct', just not used linguistically].