
tauschen
to exchange / swap
To give away an object, a service, or a position and receive something else in return from another person.
Die Kinder tauschen auf dem Schulhof ihre Sammelkarten.
The children swap their trading cards in the schoolyard.
to exchange / swap
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to exchange / swap
To give away an object, a service, or a position and receive something else in return from another person.
Die Kinder tauschen auf dem Schulhof ihre Sammelkarten.
The children swap their trading cards in the schoolyard.

to be mistaken
An outdated or elevated way of saying 'sich täuschen' (to be mistaken); to make an error or be wrong in an assumption.
Wenn ich mich nicht tausche, haben wir uns schon einmal getroffen.
If I'm not mistaken, we have met before.
When exchanging or swapping, the preposition 'mit' is often used for the person and 'gegen' for the item you receive in return. You can also simply use two accusative objects if the person is clear.
Ich tausche meinen Apfel gegen deine Banane.
I'll trade my apple for your banana.
Common things that people 'tauschen' are 'Plätze' (seats), 'Rollen' (roles), 'Telefonnummern' (phone numbers), or 'Blicke' (glances). It often describes a mutual action in which both parties give and take something.
Können wir bitte die Plätze tauschen? Ich möchte am Fenster sitzen.
Could we please swap seats? I'd like to sit by the window.
The reflexive form 'sich tauschen' for 'sich irren' (to be mistaken) is elevated and somewhat outdated. It is mainly found in written language, often in the fixed phrase 'wenn ich mich nicht tausche' (if I'm not mistaken).
Wenn ich mich nicht tausche, ist das der Herr Meier von gegenüber.
If I'm not mistaken, that is Mr. Meier from across the street.
to change / switch
Wechseln generally refers to moving from one place to another; it does not require another person to be involved. Tauschen, on the other hand, means that two people give up their places to each other and each take the other person's place.

Nach der Pause tauschen Mia und Lea ihre Plätze.
After the break, Mia and Lea swap seats.
Nach der Pause wechselt Mia auf einen freien Platz am Fenster.
After the break, Mia moves to an empty seat by the window.