diretonic The source that lilypad referenced is correct about the interval C# to Eb. It's called a diminished 3rd.
It is not a third though.
That is - it is not a third -- unless for example (which is actually not going to happen) we define and actually somehow use another scale (eg. a different scale) - such as a 'semitone scale' ....... based on all twelve notes in full sequence.
eg. C, C#, D, D#, E, F, F#, G, G#, A, A#, B
But that sort of semitone 'scale' is not what I or maybe a bulk of people actually use for their piano music - that sort of scale. Although - we or some people often will run that semitone sequence up and down the piano for finger and thumb exercises etc.
We generally just deal with the minor scale and/or major scale.
And for those scales (major or minor) - thirds of any sort are based on (depending on perspective) span of three notes, or can be based on relative degree of a higher note in relation to a lower note - where the lower note can temporarily be used as a tonic/root of the major or minor scale of its own letter name (in this case, third degree will be where the higher note is located - relative to the temporary tonic).
It pretty much means that a 'diminished third' is not a 'third' in our popular scale system.
In other words, a 'diminished third' does not mean that the result of diminishing a third is another 'third'. It means that we end up with an interval that is no longer a 'third' after we carry out that operation on a minor third.
Or in other words - in our system, a 'diminished third' is actually a major second interval in our major/minor scale system. And a diminished third is not a type of 'third'.
