Modes are named collections of specific notes, usually played sequentially, that emphasize a certain root. The unordered collection of notes in a single scale can have multiple modes with different names, where each note in the scale is the root of a different mode. More
(See Diatonic Modes & Chords for a detailed explanation.)
For example C Ionian (Major) and C Mixolydian have the same root and share six notes (different parent scales), but differ by one note (F for the former, F# for the latter), or C Ionian (Major) and G Mixolydian, which have the same notes (the white keys on the keyboard) but a different root (C v. G).
Jazz theory generalizes modes, allowing their notes to be played simultaneously, blurring the distinction between chord and scale. Groups of similar chords with the same root are collected into modes (said to be compatible, Levine 1995), so for example, the C Mixolydian mode is “played” vertically by voicing (or played over) either a C major triad, a C dominant seventh, or a C dominant ninth, etc.