The weights are the model
When training is finished, the architecture of the network (how many layers, how many neurons, how they're connected) hasn't changed. What changed are the weights.
A trained model is its weights. Nothing more. Billions of numbers, arranged in a specific configuration, encoding whatever pattern the network extracted from its training data. There are no rules written inside it. No lookup table. No explicit knowledge a human could read. Just numbers.
When researchers share a model or deploy one to a server, what they're actually moving is a file full of those numbers. The architecture is a fixed container. The weights are what fills it.