The funicular process is an embryological remnant that is usually atritive and closed.
Occasionally it is still open or partly open in a paediatric patient such as a patent processes vaginalis,
Occasionally it can be partly open in an adult such as an encysted hydrocele.
The case I suspect you are thinking about is the patient with epididymitis that is involving an encysted hydrocele. In this case I would call it “epididymitis with involvement of an encysted hydrocele” rather than funiculitis.
The term vasitis I also don’t tend to use, although I can see why I should be tempted to. I guess all bacterial epididymitis must come down the vas so anatomically its is visits. I still just use the term epididymitis. I may also indicate what level the infection has reached, for example reaching the tail of the epididymis or reaching the body or head etc.
I wonder if I should use the word vasitis when it has not quite reached the epididymal tail, however by calling it epididymitis everyone knows what I mean and the treatment is the same. (a good dose of weed killers)