The seven modes of the Major scale are almost always defined as follows:
Ionian: the scale obtained when starting a major scale from the 1st degree (that’s the major scale itself)
Dorian: the scale obtained when starting a major scale from the 2nd degree
Phrygian: the scale obtained when starting a major scale from the 3rd degree
Lydian: the scale obtained when starting a major scale from the 4th degree
Mixolydian: the scale obtained when starting a major scale from the 5th degree
Eolian: the scale obtained when starting a major scale from the 6th degree
Locrian: the scale obtained when starting a major scale from the 7th degree

Applying the definitions above using the C major scale, we get:
C Ionian: C D E F G A B C
D Dorian: D E F G A B C D
E Phrygian: E F G A B C D E
Etc…

Similarly, using A major you get:
A Ionian: A B C# D E F# G# A
B Dorian: B C# D E F# G# A B
C# Phrygian: C# D E F# G# A B C#
Etc.

In other words, you will always obtain the same seven notes of your initial major scale, and if you use these notes to try and improvise something, it will (obviously) always sound more or less the same!
So, although the definitions above are correct, they are musically irrelevant!
They are nothing more than a convenient way to obtain the notes of any mode.
For example: suppose we are looking for the notes of Eb Lydian. Since the Lydian mode is the 4th mode of a major scale, we simply need to find the major scale whose 4th degree is Eb. That’s the Bb major scale: Bb C D Eb F G A Bb. The Eb Lydian mode is therefore: Eb F G A Bb C D.

If we want to make the modes musically significant, we need to compare them using a common reference. For example, taking C as the tonal center, we have:
C Ionian: C D E F G A B C
C Dorian: C D Eb F G A Bb C
C Phrygian: C Db Eb F G Ab Bb C
C Lydian: C D E F# G A B C
C Mixolydian: C D E F G A Bb C
C Eolian: C D Eb F G Ab Bb C
C Locrian: C Db Eb F Gb Ab Bb C

If we notate the major scale (Ionian mode) 1 2 3 4 5 6 7, then in comparison:
Dorian: 1 2 b3 4 5 6 b7
Phrygian: 1 b2 b3 4 5 b6 b7
Lydian: 1 2 3 #4 5 6 7
Mixolydian: 1 2 3 4 5 6 b7
Eolian: 1 2 b3 4 5 b6 b7
Locrian: 1 b2 b3 4 b5 b6 b7

Or, using an intervallic description with W = Whole tone and H = Half tone:
Ionian: W W H W W W H
Dorian: W H W W W H W
Phrygian: H W W W H W H
Lydian: W W W G W W H
Mixolydian: W W H W W H W
Eolian: W H W W H W W
Locrian: H W W H W W W

These could equally be used as definitions of the seven modes; in fact, they would even be better definitions than the ones that are commonly used and that we started with, because they make it clear that modes are fundamentally different organizations of the seven pitch classes. But since they are admittedly more difficult to commit to memory, these definitions are rarely used.
However, that’s how modes should be understood and used.

To conclude, I strongly recommend this little gem on YouTube. During a little less than an hour, the über-famous conductor Leonard Bernstein goes about explaining and demonstrating the modes to his audience…
A must see!