die Verwechslung
mix-up
A mistake in which a person or thing is wrongly taken for another.
Entschuldigen Sie, das war eine Verwechslung, ich dachte, Sie wären Herr Meier.
Excuse me, that was a mix-up; I thought you were Mr. Meier.

mix-up
Loading your saved state.
mix-up
A mistake in which a person or thing is wrongly taken for another.
Entschuldigen Sie, das war eine Verwechslung, ich dachte, Sie wären Herr Meier.
Excuse me, that was a mix-up; I thought you were Mr. Meier.

'Verwechslung' (mix-up) comes from the verb 'verwechseln' (to confuse / mix up). The prefix 'ver-' here indicates an error or misunderstanding, and 'wechseln' (to change / exchange) describes the exchange. The ending '-ung' forms the noun for this process.
Durch eine Verwechslung der Namen erhielt die falsche Person den Preis.
Because of a mix-up of the names, the wrong person received the prize.
If you want to say what was confused with what, you use the structure 'Verwechslung von A mit B' (confusion of A with B). Here, 'A' stands for the person or thing in front of you, and 'B' for the one you think it is.
Die Verwechslung von Salz mit Zucker hat den Kuchen ungenießbar gemacht.
The mix-up of salt with sugar made the cake inedible.
The expression 'zum Verwechseln ähnlich' (confusingly similar) is a fixed expression. It is used to describe an extreme similarity and usually comes directly after the adjective 'ähnlich' (similar).
Diese Kopie ist dem Original zum Verwechseln ähnlich.
This copy is confusingly similar to the original.
mistake / error
'der Fehler' and 'die Verwechslung' can both have to do with a mistake. 'der Fehler' is the general word: a statement, decision, or action is not correct. 'die Verwechslung' is more specific. It happens when you take one person or thing for another, for example two names, bags, or appointments. Learners may confuse the words because a mix-up is often also a mistake. But not every mistake is a mix-up. When it is about incorrect calculations, incorrect grammar, or a bad decision, 'Fehler' fits. When two similar things get mixed up, 'Verwechslung' fits.

Im Hotel gab es eine Verwechslung, weil zwei Gäste denselben Nachnamen hatten.
There was a mix-up at the hotel because two guests had the same last name.
Adam macht beim Ausfüllen des Formulars einen Fehler in der Adresse.
Adam makes a mistake in the address while filling out the form.