kreischen
to scream
To let out a very high, loud, and often shrill cry, usually from excitement, fear, or pain.
Die Fans kreischten, als die Band endlich auf die Bühne kam.
The fans screamed when the band finally came on stage.

to screech / scream
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to scream
To let out a very high, loud, and often shrill cry, usually from excitement, fear, or pain.
Die Fans kreischten, als die Band endlich auf die Bühne kam.
The fans screamed when the band finally came on stage.

You can tell whether a person or a thing 'kreischt' (screeches/screams) from the subject of the sentence. If people or animals are the subject, they let out a high-pitched cry. If the subject is an object, it produces a loud, squealing sound.
Die Kinder kreischten vor Freude auf der Achterbahn.
The children screamed with joy on the roller coaster.
When people 'kreischen' (scream), it often happens because of a strong emotion. This is frequently expressed with the preposition 'vor' + dative, for example 'vor Lachen kreischen' (to scream with laughter), 'vor Schreck kreischen' (to scream in fright), or 'vor Begeisterung kreischen' (to scream with excitement).
Er erzählte einen so guten Witz, dass wir alle vor Lachen kreischten.
He told such a good joke that we all screamed with laughter.
When describing sounds, 'kreischen' (to screech) is typically used for mechanical or friction noises. Common subjects are 'Bremsen' (brakes), 'Reifen' (tires), 'eine Säge' (a saw), 'eine Tür' (a door), or 'Möwen' (seagulls).
Die alte Gartentür kreischt bei jeder Bewegung.
The old garden gate screeches with every movement.
to scream
'schreien' and 'kreischen' both describe loud sounds caused by strong emotions. 'schreien' is more general and can be high or low, short or longer. It fits fear, pain, anger, or great joy. 'kreischen' is more specific: the sound is very high-pitched, shrill, and often unpleasant. That is why 'kreischen' is used especially for sudden fear, pain, or great excitement. The words can be confused because 'kreischen' can be a kind of 'schreien'. If you want to emphasize the high, shrill sound, 'kreischen' is more precise.

Auf der Achterbahn kreischten wir vor Aufregung.
On the roller coaster, we screamed with excitement.
Am Abend schrie das Kind, weil es sich den Finger eingeklemmt hatte.
In the evening, the child screamed because it had caught its finger.