A media player is the device that actually runs the signage software and outputs to the screen. It is either a small external box connected by HDMI, or a system-on-chip built into a commercial display so there is no separate unit at all.
The trade-off between them is lifespan against simplicity. Built-in SoCs mean nothing to mount, power or steal, and a single warranty, but the processor ages faster than the panel, so a mechanically fine screen can stop running current software years before it needs replacing. External players can be upgraded independently, at the cost of another device per screen to install and manage.
The caveat is that the player, not the screen, determines what the network can actually do. Smooth 4K, several independently-updating zones, live data and web-based content all sit on the player's capability, and it is the component most often under-specified because it is invisible in the finished install.
Test the layouts you intend to run on the exact player being deployed, under continuous playback for at least a few days. Memory leaks and thermal throttling are the two failures that never appear in a demo and always appear in month three.