That model has 8 PoE ports on it. I've installed a couple of them, so I know what I've hooked up. Or at least the ones I purchased had 8. Perhaps there isn't a model number denotation between 4 and 8 port. New models denote the difference, that is an old recorder so it could have been different.
What you are finding is pictures of an 8 channel with 4 PoE. This means you can put 4 IPCs on the PoE switch, their others must be powered by other means and must reside on your main LAN segment. Hikvision limits the number of devices allowed on built in switches to the number of ports physically in existence. I installed a 32CH recorder last year that has 16 PoE, the other 16 cams could not be on that switch even with another switch daisy chained to it. They refused to connect. Networking rules tell you that's permitted, Hikvision rules said no.
Avoid the SE model. That's old and is starting to fade in firmware support. Get an E model or I model. I is most current, supports 4K but is a bit pricey.
7600 is the series on both of these. The last 2 digits are the channel count. E1 and E2, to my knowledge, the E is the hardware revision (like SE), and the number indicates the number of drives it can hold (1 SATA or 2 SATA), but an 8P suffix means it has 8 PoE ports. E1/4P has 1 hard drive and 4 PoEs as you indicated. The only major difference I noticed was the E series on up have USB3, whereas the SE model is older and only has USB2. I've installed several of both and many 7700 series units as well.
To simplify everything, get a DS-7608NI-E2/8P. 8 cameras, 8 ports. Doesn't get any simpler than that.
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