Compressed air couplers are part of the compressed air user tag team, the couplers and the connectors.
If you have threaded a air line connector into the supply port of each of your air tools, which is what you want to do to be able to supply compressed air to them quickly, those connectors allow quick connection of an air tool (or any other air component, for that matter) to a mating coupler on an air supply hose.
In the photo below, all of the couplers are from the same manufacturer, each has a different method of being connected to an air hose or air appliance.
Item 1 shows an NPT thread, item 2 is a female NPT thread and item 3 is a barbed fitting.
When you are buying couplers you have to make sure that the internal configuration of the new coupler (inside of item 4) matches the external shape of the mating connector. In order for the coupler to connect properly to the connector, they must be of compatible design. If not, you may not be able to insert your connector into the coupler, or if you can, it is possible that the two will blow off when you least expect it.
There are some industrial standards for couplers and connectors. It is unfortunate that it is often the case that a coupler from one company won't fit the connector from another company, and the reverse is true as well.
What I normally do is select one brand from my local outlet, buy lots of couplers and mating connectors, and then discard all of the others that do not connect, or are suspect. Do yourself a favor and only keep compatible brands of couplers and connectors in your tool crib or tool box.
For the industrial user, you can purchase quality couplers and connectors from your industrial compressor distributor or industrial supply house. Same rule applies. Only keep compatible brands in stock. Otherwise you'll always grab the wrong one when working on a new application, necessitating a trip back to the tool crib and wasted time.
How do you side load a coupler/connector? It is pretty hard not to, sometimes.