There's a massive difference. In fact, the data describing the trained model is not at all analogous to a cryptographic key.
A cryptographic key is a piece of information which, as long as it remains secret, should be sufficient to protect the confidentiality and integrity of your system. This means that your system should remain secure even if your adversary knows everything else apart from the key, including the details of the algorithm you use, the hardware you have, and even all your previous plaintexts and ciphertexts (inputs and outputs). If the key fails to have this property, your cryptosystem is broken.
The trained model (or the weights of a NN) does not have this property at all. Keeping the model secret does not ensure the confidentiality or integrity of the system. E.g. just knowing some inputs and outputs of the secret model allows you to train your own classifier which behaves similarly enough to let you find perceptual hash collisions. If you treat your model as a cryptosystem, this would be a known-plaintext attack: any system vulnerable to these is considered completely and utterly broken.
You'd have to keep all of the following secret: the model, all its inputs, all its outputs. If you manage to do that, this might be secure. Might. But probably not. See also Part 2 of my FAQ, which happens to cover this question. [1]
[1] https://news.ycombinator.com/item?id=28232625