to cope / get by
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to cope
To successfully manage a situation, a task, a person, or a new environment; to find one's way in it or get along well with it.
Kommst du mit der neuen Software gut zurecht?
Are you coping well with the new software?
'Zurechtkommen' (to cope/get by) is a separable verb. The prefix 'zurecht-' comes at the end in a main clause. In a subordinate clause, the verb stays together, and in the infinitive with 'zu', 'zu' goes in the middle.
Er kommt in der neuen Stadt gut zurecht.
He is getting by well in the new city.
In the main meaning 'etwas bewältigen' (to manage something), 'zurechtkommen' (to cope) is almost always used with the preposition 'mit' (with) and the dative. You cope 'mit' (with) a person, a thing, or a situation.
Sie kommt mit ihrem neuen Chef nicht gut zurecht.
She doesn't cope well with her new boss.
The meaning 'rechtzeitig ankommen' (to arrive in time) is very rare today and is considered outdated. In modern language, the word is used almost exclusively in the meaning 'etwas bewältigen' (to manage something).
Er beeilte sich, um vor dem Regen noch zurechtzukommen.
He hurried in order to arrive in time before the rain.
to manage / create
'schaffen' and 'zurechtkommen' can both have to do with coping with a situation. 'schaffen' is used when a specific task is completed or a goal is reached. 'zurechtkommen' is used more when someone can deal with a situation, a person, an environment, or a task in everyday life. It is not always about a clear endpoint, but about whether you are managing or coping. Learners may confuse the words because both can say that something is not too difficult. For a single task, 'schaffen' usually fits. For a longer situation or a new environment, 'zurechtkommen' is better.
Mein Nachbar kommt am Wochenende gut ohne Auto zurecht.
My neighbor manages well without a car on weekends.
Er schafft den Bericht heute zu Hause, weil es dort ruhiger ist.
He will finish the report at home today because it is quieter there.