I don't think they work the same way, but I think they work in ways that are close enough in function that they can be treated the same for the purposes of this conversation.

Pen and pencil are "the same", and either of those and printed paper are "basically the same".
The relationship between a typical modern AI system and the human mind is like that between a pencil written document and a word document: entirely dissimilar in essentially every way, except for the central issue of the discussion, namely as a means to convey the written word.

Both the human mind and a modern AI take in input data, and extract relationships and correlations from that data and store those patterns in a batched fashion with other data.
Some data is stored with a lot of weight, which is why I can quote a movie at you, and the AI can produce a watermark: they've been used as inputs a lot. Likewise, the AI can't perfectly recreate those watermarks and I can't tell you every detail from the scene: only the important bits are extracted. Less important details are too intermingled with data from other sources to be extracted with high fidelity.