Procuratorial vs Prosecute - What's the difference?

As an adjective procuratorial

is of or pertaining to a procurator or proctor.

(legal) to start criminal proceedings against.

(-)

Of or pertaining to a procurator or proctor.

(Ayliffe)

(Webster 1913)

(prosecut)

(legal) To start criminal proceedings against.

to prosecute a man for trespass, or for a riot

* Milton

To acquit themselves and prosecute their foes.

(legal) To charge, try.

To seek to obtain by legal process.

to prosecute a right or a claim in a court of law

To pursue something to the end.

to prosecute a scheme, hope, or claim

* Shakespeare

I am beloved of beauteous Hermia; / Why should not I, then, prosecute my right?

* prosecutable