The first balloon was probably a flat paddle balloon with a pear shape. The pear shape persists in many party balloons even those made on full molds. Molds can be a flat paddle like you might cut out of cardboard, or a full machined shape, or a fluted shape which is a compromise and made typically with 4 flutes like two paddle balloon molds joined together down the center. Some balloons such as punch balls can be made with more flutes. There have been "super round" balloons made with as many as 16 flutes.
Round balloons can also be spherical and lose the pear shaped taper into the neck area. These will often be made on fluted molds (and often when just filled with a bit of air and not yet inflating they will be almost box shaped).
The other popular balloon shape is the airship. It is cylindrical and inflates like a long tube, and starts out like a long tube. The most common of these is the twister balloons designed for people who make balloon animals. However there are sizes much larger than these long thin balloons. Variations include the Jelly Bean balloons which were short and very fat and huge airship balloons that can blow up seven feet long and ones that can inflate to two feet in diameter down their entire length.
The blimp or Zeppelin shape is also long but it is not cylindrical. It bulges in the center or middle part of its length. One of the most remarkable was made by Tilly and had a rounded nose. Though rated at 12 inch by 40 inches it could inflate to over five feet and get 15 inches in diameter largely due to its well designed profile. Most blimp balloons now tend to have a more pointed end.
Another variation is the knobby balloon. This is an airship which is somewhat like a string of small balloons grafted together and inflates as it initially looks, like a series of bulges end to end. The most extreme example of this was "The Worker Balloon" which was seen at state fairs and similar venues. It was a huge balloon that could inflate almost 12 feet long and really attracted attention for the balloon sellers who were "working" the crowd. However the balloons they sold were smaller versions of similar knobby balloons.
The Geo balloon is a very clever balloon which has a hole in it. It is donut shaped. When the machine is working correctly they can be very good but they have a tricky seam that can sometimes be a weak spot. A variation was the "petal" shape which was like a knobby donut. They were made in both a tiny 6 inch size and a 16 inch size.
Two basic types of balloons have ears. The mouse ear balloons which tend to have ears like two smaller balloons grafted onto the larger "head" balloon and the cathead balloons which are now rare and had longer tapered ears. The heart shaped balloon is basically the same thing but with ears that are quite fat and short so when inflated the balloon adopts a heart shape. All such balloons are weak between the two "ears".
The doll balloon is basically two balloons grafted together, a pear shaped large body one and a smaller round one for the head. Doll balloons tend to be rare. A company in Canada made them years ago designed to inflate about four to five feet tall. Giant doll balloons are still made and can inflate taller than that and MUCH fatter.
After these basic shapes you have a wild array of animal and other shapes lumped together as "figurine" balloons. They often have a number of sections grafted together and can be quite large.
Any time a balloon has more than one section or even an abrupt transition from the body to its neck, it runs into physics. It takes more pressure to inflate a small diameter than a large one. In the larger section the pressure trying to stretch the latex gets to work on more square inches inside and thus exert more total force on the latex making it stretch.
This means such balloons are difficult to inflate. It is not easy to design something like a mousehead balloon that can just be put on a pump and inflated with the ears inflating on command without the body bursting first. The same for a doll balloon where getting the head to inflate before the body just bursts trying is tricky.
Complex balloons can be a real challenge to figure out how to inflate. Of course you can just hook one up to a compressed gas source and hope and if the design is well done each part should inflate in turn, often with a sudden whoomp. That is because once the smaller part starts to inflate, it actually becomes easier to blow up so the overpressure built up trying to get this smaller area to inflate gushes into it until the stress equalizes again.
An interesting experiment was the Playloon. It was designed to be inflated to 30 to 36 inches and heavy gauge latex so it could withstand more rough handling than a typical balloon. While they were available they were a favorite type among balloon collectors.
The size of a balloon can be stated several ways depending on the shape. Extra round fluted balloons would be sized as to rated inflation diameter. The more pear shaped balloons would be rated for the diameter at the widest point at rated inflation size. The long balloons such as blimps and airships are typically rated for the length they should reach when properly inflated. Sometimes by two numbers, the rated length and the rated diameter when properly inflated.
Measuring the diameter of a balloon can be tricky. Smaller size balloons inflated in mass for decorating are often sized by some kind of template, or a pair of rods sticking up from a stand the desired distance apart for the rated diameter. There is even a very cleaver cloth collapsable box available with a number of different size holes in its six sides.
However a tape measure works extremely well. You measure the circumference. Then just divide by 3.14 to get the diameter. It is easy to find 60 inch tape measures. If you look under sewing supplies used by quilters you can find 100 inch and 120 inch tape measures. For really large balloons you can overlap and glue two of the 120 inch tape measures together with the second one starting at the 100 inch mark on the initial one. This way it will go up to 220 inches in diameter.
A 60 inch tape measure is good up to 19 inches in diameter. Often you can find cloth in this size. But then tend to have metal ends and do not do well with the ends removed. Fiberglass tape measures can easily have the metal ends removed but be careful how you fold them up. Roll them into a large diameter roll for storage. They will take a set and then curl and knot themselves and be difficult to use.
The 100 inch tape measure is good up to 31 inches. The 120 inch is good up to 38 inches. If you double a pair of 120 inch tape measures together at the 100 inch point (so you do not have to do any math in your head other than add 100 for the second length of tape) it can be used up to 70 inches. But at about 40 inches it can be quite difficult to get the tape around a balloon by yourself.
Measuring with a tape measure is quite accurate because any errors are divided by 3. You can often find tape measures today which have inches on one side and cm on the other. So this trick passes the International Friendly test.
For most balloons the 100 inch tape measure is a good size. The 60 inch works well for any common size balloon or party balloon. The idea of measuring by circumference and then dividing by 3.14 also only requires an easy to store tape measure. Though you might want to get out the spreadsheet and make a chart of sizes of interest and the circumference required or organized however best suits your interests and print it out. Exceptional people can of course divide by 3.14 in their heads. Or just divide by 3 and apply "fudge factor", mas or menos, close enough for government work etc.