My 100% baseless opinion is that animal brains are fundamentally different from computers, although they might share some characteristics (like, we can do maths right?).
If I understand it correctly, biological brains are essentially associative memory machines where memory and computation are intertwined into one physical structural system.
In short: To think is to remember. And to remember is to think.
You are correct in that opinion.
I’m not or specialist in the field, but FWIW key difference between neural circuit vs processor is that former is specialised and analog while latter is programmable and digital.
Your brain is not running any software, instead its hardwired to process series of electric signals („trains”). Neurons can be used to model logic gates, but nature uses different approach where there are „dumb” neurons that just transmit signals and then there are „functional” neurons that emit signal only if certain conditions have been met, be it right frequency of electric signals in „electric train”, current chemical state of neuron or number of received signals from other neurons at given time.
At some levels, you could trivially describe a CPU this way too.
I would be wary of any level of confidence about "what brains do".