die Einberufung
call-up
The official request for a person to begin military service or civilian service.
Er erhielt den Bescheid für seine Einberufung zur Bundeswehr.
He received the notice for his call-up to the German armed forces.

call-up / convening
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call-up
The official request for a person to begin military service or civilian service.
Er erhielt den Bescheid für seine Einberufung zur Bundeswehr.
He received the notice for his call-up to the German armed forces.

'Einberufung' (call-up / convening) is the nominalization of the separable verb 'einberufen' (to call up / to convene). The verb consists of 'ein-' and 'berufen' (to call/appoint someone) and means to 'call' someone into a group or into service.
Die Firma kann eine Sondersitzung einberufen, wenn es nötig ist.
The company can convene a special meeting if necessary.
You can recognize the meaning from the context: If it is about the military, compulsory military service, or civilian service, it means the request to report for duty. If it is about bodies, meetings, or assemblies, it means the formal calling together.
Die Einberufung zum Wehrdienst kam für ihn überraschend.
The call-up for military service came as a surprise to him.
In a military context, one receives an 'Einberufungsbefehl' (call-up order) or 'Einberufungsbescheid' (call-up notice). The request itself is the 'Einberufung zum Wehrdienst' (call-up for military service).
Mit dem Einberufungsbefehl musste er sich bei der Kaserne melden.
With the call-up order, he had to report to the barracks.
When a meeting is convened, the body often appears in the genitive or with the preposition 'von' (of). Typical verbs are 'fordern' (to demand), 'beschließen' (to decide), or 'beantragen' (to request/apply for).
Der Vorstand beschloss die Einberufung der Mitgliederversammlung.
The board decided on the convening of the members' meeting.
invitation
'Einladung' and 'Einberufung' are both requests for someone to come somewhere or take part in something. However, 'Einladung' usually sounds friendly and voluntary, for example for a celebration, a visit, or an event. 'Einberufung' is much more formal and official. It fits military service, civilian service, or the calling together of a body or committee. The words can be confused because both mean that someone is supposed to come. As a practical rule: in private or normal social situations, you say 'Einladung'; for official duties or formal meetings, 'Einberufung' is more likely.

Die Einberufung des Ausschusses erfolgt nächste Woche schriftlich.
The convening of the committee will take place in writing next week.
Meine Schwester schickt heute die Einladung zu ihrer Geburtstagsfeier.
My sister is sending the invitation to her birthday party today.