
getrennt
separate
Not together in terms of space; separated from one another.
Die beiden schlafen in getrennten Zimmern.
The two sleep in separate rooms.
separate / separated
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separate
Not together in terms of space; separated from one another.
Die beiden schlafen in getrennten Zimmern.
The two sleep in separate rooms.

separated
Refers to a couple that has ended their partnership or shared life together but is not yet legally divorced.
Meine Tante und mein Onkel leben seit einem Jahr getrennt.
My aunt and uncle have been living separately for a year.

separate
Individually or separately, not together. Often used in the context of payments.
Wir möchten bitte getrennte Rechnungen.
We would like separate bills, please.
'Getrennt' (separate/separated) is the past participle of the verb 'trennen' (to separate). It is very often used as an adjective to describe a state of separation.
Die beiden Gruppen wurden getrennt voneinander untergebracht.
The two groups were accommodated separately from one another.
If you want to express what something or someone is separated from, you use the preposition 'von' with the dative.
Seit dem Umzug lebt er getrennt von seiner Familie.
Since the move, he has been living separately from his family.
In a restaurant, the question 'Zusammen oder getrennt?' (Together or separately?) is very typical. If you do not want to pay together, you answer 'Getrennt, bitte!' (Separately, please!) or say 'Wir möchten getrennt zahlen.' (We would like to pay separately.)
Kellner: „Zahlen Sie zusammen oder getrennt?“ - Gast: „Getrennt, bitte.“
Waiter: 'Are you paying together or separately?' - Guest: 'Separately, please.'
In the context of couples and relationships, 'getrennt leben' (to live separately) or 'getrennt sein' (to be separated) means that the relationship has ended, but the people are not yet divorced.
Sie sind seit letztem Herbst getrennt und werden sich bald scheiden lassen.
They have been separated since last fall and will soon get divorced.
individual / separate
Einzeln and getrennt can both express, when paying, that something is not done together. Einzeln focuses more on each person or bill being handled separately and often one after another, whereas getrennt emphasizes dividing the payment into separate bills. In a restaurant, getrennt is especially appropriate when each person is supposed to pay for themselves.

Wir baten den Kellner, die Rechnungen getrennt auszustellen, damit jeder selbst bezahlen konnte.
We asked the waiter to issue separate bills so that everyone could pay for themselves.
Der Kellner nahm die Rechnungen einzeln entgegen und kassierte sie nacheinander.
The waiter took the bills one at a time and collected the payments one after another.