Dim really means dim7
In popular music diminished invariably means a diminished 7th (dim7) chord. Sometimes a diminished 7th chord is indicated, but usually not. However when a diminished chord is indicated a diminished 7th chord should, or at least could, be played.
Lower one note
Lowering any one of the four notes in a diminished chord will change that chord to a dominant 7th chord. This is one reason why diminished chords are so good at changing the direction of the music.
Raise the root
A diminished chord can be created by lowering the 3rd, the 5th, and the 7th in a dominant 7th chord, or the chord can be created by adding a stack of minor 3rds to the root, or create a diminished chord by raising the root in a dominant 7th chord
Build using mid points
Here is another way. Start with 2 notes an octave apart. I will use C in this example. Find the note that is midway between the 2 Cs; it is F#. Now find the note that is midway between C and F#; it is Eb. Now find the note that is midway between the F# and the upper C; it is A. The notes we have found are C Eb F# A C. That is a diminished chord.
Tritones
In the example above the C F# interval is a tritone (three tones) and the upper interval F# C is also a tritone. Skipping a note in a diminished chord will produce a tritone so Eb to A is a tritone too. Tritones come with baggage. They were banned in early church music. They have been called the forbidden chord or the devils interval. However over time they have not only become acceptable, they have become indispensable. They have evolved from being forbidden to being valued, and they are widely used in modern music.
Wrong spelling
In popular music most diminished chords are spelled incorrectly. A diminished chord is created by lowering the 3rd the 5th and the 7th in a dominant 7th chord.
C dim is usually written C, Eb, F#, A. The F# is wrong because the lowered 5th is Gb. The A is wrong because the lowered 7th is Bbb. The A is actually the 6th. But, A dim has exactly the same notes, the A is the root and has to be named A. This could all get confusing so a pragmatic approach is taken and dim chords are always spelled the same way. So, if a new diminished chord using the same notes is viewed as an inversion or as a chord with a different root, the name of each note remains the same.