der Gast
guest
A person whom you invite to your home or to an event and entertain or provide hospitality for.
Wir erwarten heute Abend Gäste zum Essen.
We are expecting guests for dinner this evening.

guest
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guest
A person whom you invite to your home or to an event and entertain or provide hospitality for.
Wir erwarten heute Abend Gäste zum Essen.
We are expecting guests for dinner this evening.

A 'Gast' (guest) at home is an invited person. A 'Gast' (guest/customer) in a restaurant or hotel is a paying customer. The context (private or business) determines the exact meaning.
Meine Eltern haben am Wochenende Gäste zum Kaffee da.
My parents are having guests over for coffee at the weekend.
'Gast' (guest) is often used as the first part of compound words to describe a temporary role. Examples include 'der Gastarbeiter' (guest worker), 'der Gastprofessor' (visiting professor), or 'der Gastauftritt' (guest appearance).
Die Universität hat für dieses Semester einen Gastprofessor aus Japan eingeladen.
The university has invited a visiting professor from Japan for this semester.
The expression 'zu Gast sein' (to be a guest) is very common and means that someone is temporarily present at a place or at an event. It is often used with the preposition 'bei' (at/with) or 'in' (in).
Nächste Woche ist eine berühmte Autorin in unserer Schule zu Gast.
Next week, a famous author will be a guest at our school.
member
'das Mitglied' and 'der Gast' can both be people in a group, at an event, or in a club. The important difference is belonging. A 'Mitglied' permanently belongs to a group or organization. A 'Gast' is only there for a certain time, for example because they have been invited or are taking part in an event. Learners may confuse the words when both people are in the same place. In practice: someone who belongs is a 'Mitglied'. Someone who is only visiting or temporarily taking part is a 'Gast'.

Zur Versammlung dürfen die Mitglieder auch einen Gast mitbringen.
Members are also allowed to bring a guest to the meeting.
Seit Januar ist Lena Mitglied im Sportverein.
Lena has been a member of the sports club since January.