Give two very different things the same name and soon enough many people will believe them to be the similar in nature.

If you repeat the lie often enough if will become the truth.

Not really a lie, just biomimicry. The full name is "artificial neural network" after all.

It's a lot closer to biology than the steam engine or clockwork watch.

Abstract algebraic equations are not closer to biology than the steam engine or clockwork watch.

The latter are at least physical. Gradient descent and inference doesn’t resemble the physical mechanisms that drive neurons at all. Floats and integers aren’t even capable of representing a continuous voltage potential.

There is zero relation between a "neuron" in neural networks and a real neuron. It's entirely marketing. The field of "AI" has always been quick to market their work as magic rather than be open and honest about the reality, which is why we have been through at least 3 AI winters already.

Well, like evolutionary algorithms, the thing was designed to replicate some features of the natural one.