In principle, no, declaring the ambassador persona non grata only directly means that that particular official is no longer welcome and recognized, the state which they represented to that moment may continue to be represented on an interim basis without meaningful interruption (usually through designation of the existing deputy chief of mission as chargé d'affaires) unless the host nation also ordered the closure of the mission or formally severed diplomatic relations.
The nation whose ambassador was expelled may choose to downgrade relations formally, even if the other side has not, as its own protest, of course.
On the other hand, expelling an ambassador is a rare event and usually one piece of a fairly extreme diplomatic protest that involves other elements, either simultaneously or in close temporal proximity (fully cutting off relations or even declaring war would not be that unusual as accompanying actions.)
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In principle, no, declaring the ambassador persona non grata only directly means that that particular official is no longer welcome and recognized, the state which they represented to that moment may continue to be represented on an interim basis without meaningful interruption (usually through designation of the existing deputy chief of mission as chargé d'affaires) unless the host nation also ordered the closure of the mission or formally severed diplomatic relations.
The nation whose ambassador was expelled may choose to downgrade relations formally, even if the other side has not, as its own protest, of course.
On the other hand, expelling an ambassador is a rare event and usually one piece of a fairly extreme diplomatic protest that involves other elements, either simultaneously or in close temporal proximity (fully cutting off relations or even declaring war would not be that unusual as accompanying actions.)