Digital signage software is the whole stack that runs a screen network: the manager you publish from, the player running on each device, and the connection between them. People often mean just the CMS, but the player is half the product and the half that fails at 6am on a public holiday.
The three parts have different jobs. The manager is where content, schedules and permissions live. The player renders on the device, and must keep rendering when the network drops. The link handles updates, health reporting, and remote recovery, which is what decides whether a fault means a support ticket or a site visit.
The caveat: evaluate the player, not the demo. Demos are given on strong wifi with one screen and fresh content, which is the easiest possible case. The questions that predict real life are what the screen shows while an asset is still downloading, whether it recovers on its own after a power cut, and what happens on the device that has been offline for a week.
The blog compares the market in more depth: choosing signage software.