Lets address the first part of the question.
Per the USA Bocce Federation ( USBF ) and the International governing body for Bocce ( CIB ) the only sizes per their rules ( except Volo see below ) that are allowed for competition play are 107mm balls for men or 106mm balls for women.
So the ONLY correct sizes are
- 107mm for men
- 106mm for woman
Here I will explain the 4 “forms/variants/styles” of bocce
- Volo is played with brass/bronze balls ( can vary from 90 to 110 mm ) and has very strict rules of play. It’s the style where the balls are mostly tossed down the court. In the USA it’s the least played of the 4 styles by far. Outside the USA in France, Slovenia, Switzerland, Italy, Australia its more popular. Only played on a court approx. 90 ft long with no raised sides and marked lines across the surface.
- Raffa is played with extremely hard but resilient plastic balls. Most common style outside the USA. The rules are very formal in that a shot must be called and if balls are moved during play by mistake they are returned to their original positions. Only played on court with raised sides and marked lines across the surface.
- Open Rules was developed in the USA to “speed up the game” and to make it simpler to play. Based on Raffa style above and with the same extremely hard but resilient plastic balls. It’s the most popular style in the USA where a court is used. There is a USA National Championship for Open Rules and regular competitions around the USA at the various Bocce clubs. Courts vary in length up to 87 ft with a typical length of 70 ft, but 6o ft ( the width of a typical back yard ) is a reasonable minimum for recreational play on a backyard court. Only ever played on a court with raised sides marked lines across the surface. Balls can be and are often banked off the sides during play.
- Lastly is the game that is not played on a court but in an open area, which is often grass or sand at the beach. Most in the USA refer to this as “Bocce Ball” or Botchy, bocci, ultimate bocce, beach bocce etc Because there is no court so most of the rules for the styles above can’t apply you are actually playing Petanque (the French cousin of Bocce ) but that’s for another blog.
Now to the second part of the question.
Does it matter? You bet if you want to play at national and international level of bocce. But let’s face it, of the estimated 1,000,000 sets of bocce balls that are in the USA 99.9% of those balls never see a court. Court you say, “I thought bocce was just played on the grass or at the beach”. Well that’s what most people think. So if you are one of those and are never going to play on a court and are never going to play in any formal competition, then the ball size doesn’t matter. You fall in to category 4 above.
Hold on!! But that means if I want to play, say, football ( no not the US invention that uses a ball like a rugby ball but with totally different rules ) , the one otherwise known of as soccer. And I play at the beach with friends I can choose any size ball I want?? Sure, you probably don’t have goal posts, a goal net, marked sidelines, line judges, a referee or even 11 players per side, so why should the ball size, weight or material be the same as a regulation soccer ball?? Why because if it wasn’t you wouldn’t really want to play. The rest of the “stuff” of play can be omitted and even the rules simplified to suit the day but the ball, it has to be the real thing. Otherwise it’s little more than “kick the can”
Stick ball is NOT baseball, Baseball is NOT Softball but the game play is all very similar. One player holds a long round shaft and tries to hit a ball thrown by another player, as far as they can, then runs a distance to and fro to get points …….. But every person in the USA knows what the equipment is for those more mainstream US games. And if you tried to introduce one piece of equipment from say stick ball into softball, no one would be fooled. But with Bocce there is so much misinformation that few really have a clue about what a bocce ball size should be or what it’s made of.
For kids water filled balls are fine just as a plastic bat and a wiffle ball are fine if they are playing “baseball”.
For kids 80mm and 100mm balls made of soft plastic or even the Chinese balls made from cue ball material are also fine for the back yard, beach, etc.
But please copywriters, stop calling those sets deluxe, competition, tournament just because ( as noted above ) much of the US buying public doesn’t know the truth so can’t call you on it.
The image below, the balls are 100mm dia but they never state that even in the complete description!!!
Also balls that are 109, 110, 113 and even 115 mm are NOT tournament, regulation, certified, competition etc., balls. They are just balls brought into the USA by the big name trading houses of sporting goods that just don’t know any better. Most if not all of those products come from China. 
Everyone likes a deal. Most of us want to trust what we read and want to believe that the descriptions for products are truthful. We also want to know that important information is NOT left out.
A Louisville slugger is NOT made out of pine, it’s White Ash. If it were it certainly “should be” a lot cheaper than the real thing. Why? Because pine is cheap, in plentiful supply, easy to turn to shape, doesn’t wear out the manufacturing tooling as fast etc. And it definitely would look the part on the shelf in a store or as a photo on an eCommerce website. Especially if it was called tournament, professional, competition or even deluxe.
Sadly that is a fact of life with Bocce balls sold in the USA. They are mostly made from cheap materials, so they don’t last, crack easily, don’t roll true, turn whitish once the skin is knocked off and often retails at an inflated price. But who’s to know better??
You got this far, now YOU do.
Have a look at this link to see more about ball materials and what to avoid.
http://www.playaboule.com/bocce-ball-set-reviews.aspx
Note: This is Copyright material. Sure you can link to it and upon written approval we might let you use the wording. But please don’t just copy it.