This is a critical distinction. 

I personally feel it’s much more intuitive and accurate to call them hardware signers. I’ve had to explain to everyone I’ve set up with a hardware signer that the Sats are not on the device, they never leave the Network, and that the keys are the secret that enables them (or anyone who access to them) to move the Bitcoin. 

They really begin to understand when I walk them through the entire process and have them set up the hardware, copy the seed, and make a couple txs from exchange to self custody. And they start to understand the utility and gravity of Bitcoin at that point too.