On this same sub-forum there is
Carrier Operations Tutorial, which explains how these buttons in the task force window work for you in detail, and how to set up wings etc. .
Here is one example for a large carrier of one game:
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As you can see, the bombers and fighters are separated into groups of "Squadrons", "Formations", and the whole "Wing". There are 80 fighters and 80 bombers on board, so every squadron holds 20, the formation 40, and of course 80 for the whole wing.
Depending on how many you would want to start, you can now just click on the name and use "branch only" to start for example fighter squadron 3. If you want to launch a bigger force of 40 or 80, in this setup it is still just two clicks, as you just select the higher team name, - let's say "Bomber Formation Beta" -, and then "branch + subs", which will group all lower hierarchy craft under that name in a new TG.
You can see in the picture that I have made an even higher group ("Crafts") to draw a line around all parasite craft at once. This is helpful to setup, as it enables you to easily re-establish mothership assignment should that get messed up. It is also helpful sometimes in case you use hangar PDC.
You can also see that the carrier itself stands above all these. Technically it needn't to be there if you don't use hangar PDC, but it looks nice for overview for sure.
Then there are some singular crafts that don't get another group, because they are supposed to start alone and without formation anyway. Though they crown the Task group above anyway, in some cases it is very useful to add them here for oversight, so you can easily start them there without having to search their name in the big window above.