kriechen
to crawl
To move forward on one's stomach or on all fours with the body close to the ground.
Das Baby hat gerade angefangen, durch das Wohnzimmer zu kriechen.
The baby has just started to crawl through the living room.

to crawl / grovel
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to crawl
To move forward on one's stomach or on all fours with the body close to the ground.
Das Baby hat gerade angefangen, durch das Wohnzimmer zu kriechen.
The baby has just started to crawl through the living room.

'Kriechen' (to crawl) describes a form of movement. Therefore, the perfect tense is always formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have).
Die Schnecke ist langsam über das Blatt gekrochen.
The snail crawled slowly across the leaf.
The subject of the sentence reveals the meaning: babies or animals crawl on the ground. Traffic or time crawls when it is very slow. A person 'kriecht vor jemandem' (grovels before someone) when they behave submissively.
Das Baby ist unter den Tisch gekrochen.
The baby crawled under the table.
In the figurative, negative meaning, 'kriechen' (to grovel) is often used with the preposition 'vor' and a person in the dative: 'vor jemandem kriechen' (to grovel before someone).
Ich werde sicher nicht vor dem neuen Abteilungsleiter kriechen, nur um beliebt zu sein.
I certainly won't grovel before the new department head just to be popular.
When it is about slow movement, 'kriechen' (to crawl) is often used for vehicles in traffic jams or abstract things like time.
Die Autos krochen Stoßstange an Stoßstange über die Brücke.
The cars crawled bumper to bumper across the bridge.
four
'auf allen vieren' (on all fours) and 'kriechen' both describe moving close to the ground. However, 'auf allen vieren' is a fixed expression with 'vier' and mainly says that someone is using their hands and knees. 'kriechen' is a verb and describes the movement itself, often on the stomach or on all fours. Learners may confuse the words because in both cases the body is close to the ground. In practical terms: for the type of posture, you say 'auf allen vieren'; for the movement, you say 'kriechen'.

Nach dem Sturz musste der Wanderer ein Stück durch den engen Tunnel kriechen.
After the fall, the hiker had to crawl a short distance through the narrow tunnel.
Das Kind sucht sein Spielzeug auf allen vieren unter dem Sofa.
The child looks for their toy under the sofa on all fours.