zu dritt
in a group of three
Describes that a group consists of three people or that an action is carried out jointly by three people.
Wir waren gestern zu dritt im Kino.
There were three of us at the movies yesterday.

third
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in a group of three
Describes that a group consists of three people or that an action is carried out jointly by three people.
Wir waren gestern zu dritt im Kino.
There were three of us at the movies yesterday.

The form 'zu dritt' (as three / in a group of three) is part of a series ('allein' (alone), 'zu zweit' (as two), 'zu dritt' (as three), 'zu viert' (as four), etc.) that indicates how many people a group consists of. The expression is invariable and is used like an adverb.
Wir sind zu dritt in den Urlaub gefahren.
The three of us went on vacation together.
As the first part of a compound word, 'dritt-' means 'in third place'. In these words, 'dritt-' remains unchanged, while the second part, usually a superlative, is declined.
Er hat die drittbeste Zeit im Wettbewerb erreicht.
He achieved the third-best time in the competition.
In the construction 'jeder/jede/jedes dritte' (every third), 'dritte' is declined like a normal adjective. This expression selects an element from a regular sequence.
Jedes dritte Auto auf dem Parkplatz war rot.
Every third car in the parking lot was red.
three
'drei' and 'dritt' are both connected to the number 3, but they are used differently. 'drei' simply gives the quantity: 'drei Bücher' (three books), 'drei Personen' (three people), 'drei Tage' (three days). 'dritt' is not used just as freely. It appears, for example, in 'zu dritt' (in a group of three / the three of us) when three people do something together. In compounds like 'Drittplatz' (third place) or in forms like 'jedes dritte Mal' (every third time), it is about the third position in an order. Learners confuse the words because both have to do with 3. A simple rule is: for a quantity, use 'drei'; for a group of three people or a third position, you need forms with 'dritt'.

Nach der Arbeit sind wir zu dritt nach Hause gefahren.
After work, the three of us went home together.
Im Garten spielen heute drei Kinder.
Three children are playing in the garden today.