I was listening to Weber's Turandot Overture. A flute (or piccolo?) plays a theme, and then the entire orchestra plays the same thing. Is there a name for this?
More common in a solo concerto, this is a “tutti repeat” or “orchestral repetition”, where the entire orchestra echos the statement of a melodic subject in the solo.
No special term, beyond variations on the (perfectly clear) description you've already given. 'The theme is stated by solo flute, then repeated by full orchestra.'