How can I efficiently create this style of shape.
It's the label's shape — white cutout in the center.
I do not necessarily want to know this shape exactly, but perhaps you have seen similar shapes, generally having rounded corners and then an anchor in the center of each side is brought outward and made into a point with curves flowing naturally into the form.
Here is a picture with several examples of the shape I am desiring.
Use the pen tool. You can either draw the whole thing (which I prefer to the second option) or draw one side, duplicate and flip it horizontally and connect it back together. I personally like the slight imperfections from drawing the whole thing versus a perfectly mirrored copy of one half the drawing.
This applies to the other image you linked to as well. It might be possible to find the same or simpilar shapes on some of the free vector image sites. But by the time you find it, you could have simply drawn the thing.
Take care, Mike
Like Mike says, learn to use the Pen tool.
Also learn how to build up complex shapes from many simple ones.
Pathfinder Unite and (in newer versions Shape Builder) are your friends.
Reflect-copy can also save you a lot of work making symmetrical shapes.