The content server and cloud connections are what are called a "pull" connection, which means you use your device to pull books from the server onto your device. The content server connection requires that calibre be running on a computer somewhere that is visible on the network/internet to your device. The cloud connection requires that your library be stored in one of CC's supported cloud providers. Using one of these connections you can browse the books in your library from your device. CC puts a green check mark next to the book if it is already on your device.
The wireless device is a "push" connection, which means that you use calibre (and "talk" to calibre) to push (send) books from your laptop to CC. There is no way on CC to ask calibre to send a book when wireless device connected.
Which to choose depends on what you are trying to do. The content server connection is often better for small operations such grabbing a book or a series, or if you have a permanent calibre content server running. If your content server is set up to be visible over the internet then you can use it from anywhere in the world (the setup requires technical networking knowledge).
The cloud connection is often better than the content server if you have stored your library in the cloud.
The wireless device connection is better for larger operations such as sending many books selected in calibre using a search. It is also the way to update the metadata for all the books on the device, something you should do if you change things in calibre such as covers, tags, comments, etc. Finally, it is the way that read information is (optionally) synced back to calibre.