Certainly for a composer like Sibelius, the idea of a symphony is that it has a level of thematic integration and a working out of ideas in a logical way.
I would argue it’s actually the composers who use multiple terms, or even change their minds about a piece, that show the clearest indications of caring about the distinction. Sibelius, Holmboe... I’m sure there are others. These composers ask themselves whether they’ve created music that takes the initial thematic cells and builds a structure out of them. A kind of musical argument.
That second last sentence is not confined to the formal symphony.
Strauss Death and Transfiguration is structured as follows
There are four parts (with Ritter's poetic thoughts condensed):
Largo (The sick man, near death)
Allegro molto agitato (The battle between life and death offers no respite to the man)
Meno mosso (The dying man's life passes before him)
Moderato (The sought-after transfiguration)
A typical performance lasts about 25 minutes, so longer than the Sibelius and without the programme, that would read like the structure of a symphony. There are themes in it that appear and reappear.
For Scheherazade Rimsky wrote: ‘All I desired was that the hearer, if he liked my piece as symphonic music, should carry away the impression that it is beyond a doubt an Oriental narrative of some numerous and varied fairy-tale wonders and not merely four pieces played one after the other and composed on the basis of themes common to all the four movements.’
It has themes worked through it. Again,reading the tempi for the movements without knowing the name of the piece, I would assume it was a symphony, but it has never been referred to as one.
I suppose the world takes the lead of the composer and I am fine with that, I just wondered if there were underlying technical reasons that the world might not decide otherwise.