You may hear both terms used and they’re connected.
A cell is a single power source that provides a set amount of DC voltage, for example, a watch battery is a single cell that has a low voltage of 1.5 to 3V.
Whereas, a full battery is often a ‘stack’ of cells added together in order to create the higher voltage needed to run larger devices. This can be anything from a laptop battery to one in an electronic vehicle. Also, if you consider a mobile phone’s power bank – this is essentially a bunch of cells packed together in series to give a large storage capacity for power on the go.