There is a difference between the noun קהל (assembly) and the noun עדה (congregation), as there is a difference between מקהיל (assemble) and מיעד (appoint):

מקהיל gathers men through a voice and trumpets (and this is what distinguishes it between אסף and קבץ (collection), which also include a collection of things which have no intelligence), but מיעד is with an invitation to convene at a time.

And moreover, קהל is a gathering of the multitudes, while עדה is a gathering of the people in which their elders are in charge.

And moreover, for this reason the noun עדה refers to the Sanhedrin alone. And in particular, whenever they are mentioned together as synonyms, it will always use the noun עדה for the Sanhedrin. And also, the Sanhedrin are of the קהל when there are no rulers at that time.