When you buy a video-specific camera you get these features:
Having “Neutral Density” filters built in to the camera is a huge help. These are essentially “sunglasses for your camera” and allow you to cut the amount of lighting entering the camera so you can keep your shutter speed where you want it. Variable neutral density filters are often times the convenient way to emulate this on a mirrorless camera, but they, by nature, cut reflection, so even if their color fidelity is good, they can make skin look peculiar.
Running sound into camera is underrated. It’s so much more convenient to not have to sync in post, and many video cameras have low noise, modern pre-amps that are capable of delivering great quality if the signal coming in is hot. Dedicated video cameras have no only the inputs for connecting audio gear, but on-board physical controls for setting levels quickly. In some situations you need a separate person handling audio, but for much run-n-gun work with a single operator, on-camera audio inputs are great.
Many smaller cameras have mini headphone jack audio inputs which can also work. The bigger connections on pro video cameras are three-pin XLR. XLR allows for longer runs because it separates positive, negative and ground across three lanes. For much of what students do it likely won’t matter unless your cable run is long but it’s also a locking connector which is convenient.
False color is a very handy exposure tool. Zebras are similarly useful. Scopes, like waveform and RGB parade specifically can reveal exposure information very difficult to gauge by eye.
Peaking, magnification, etc. These functions can make focusing on a 3-inch screen much easier.
Easy to hold up to your eye or on the shoulder. I don’t care quite so much about this one generally, but you can spend a lot of time and money trying to rig up a small mirrorless camera to be more like a video camera. One thing I do find useful is the mounting points that come with the camera without requiring additional rigging.
These are essential for viewing the picture in bright sunlight if you don’t have an external monitor. The convenience of an attached EVF is something I can’t stress the importance of.
It’s recently become more common for many DSLR/mirrorless cameras to support timecode and UB recorded to a file, but they don’t allow for timecode input for “jam-syncing”. This means it’s basically just an inaccurate clock stamped over your footage but that clock doesn’t correlate with any other piece of gear.