-LAN. The LAN (Ethernet) interface was originally intended for building wired computer networks. Cameras with this connector, usually, also work as network devices. The advantage of this option over the Wi-Fi described below can be called a higher actual bandwidth, over
BNC — the ability to connect without additional equipment, directly to a standard network router used for a regular computer network. Of the shortcomings, one can only note the need to pull the wire, but this point is common to all wired connection options. For the rest of the features, LAN is the most convenient, thanks to which it has become widely used in modern security cameras.
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Wi-Fi. The Wi-Fi connection was originally a wireless analogue of the LAN described above and was used to connect to computer networks. When working in such networks, this connection is similar to LAN in the sense that it allows the camera to work through a regular router (of course, supporting Wi-Fi). At the same time, Wi-Fi is more convenient due to the lack of wires, however, with an abundance of other wireless devices connected to the router, the channel bandwidth and image quality can noticeably deteriorate. Note that recently it is also possible to use this connection in the Direct mode — for direct connection of the camera with another device, for example, connecting the camera to a smartphone (see "Design and
...capabilities — P2P"). However, this option is less common.
— BNC. Abbreviation for Bayonet Neill Concelman. A bayonet type connector commonly used for analogue video signal transmission. Refers to professional video interfaces, special equipment is required to work with such a camera. However, by themselves cameras with connectors of this type, usually, belong to the lower price range. This is due to limited connectivity via BNC — only a video signal can be transmitted through it, which limits the functionality of such cameras compared to models that work via LAN or Wi-Fi (see above).
— 3G / 4G. Internet connection via 3G / 4G mobile networks; usually, for this you need to install a SIM card from a mobile operator in the camera. The speed of such networks allows, among other things, to broadcast video in a fairly high resolution. So such a connection (of course, with coverage) is well suited not only as a fallback in case of interruptions to the Internet, but also as the main communication channel if there is no fixed Internet connection at all. A typical example of the second situation is the observation of a country house located "far from civilization", but in the zone of reliable mobile communication reception. Moreover, in both cases, you can contact the camera via the Internet from anywhere in the world. 
