That's slightly different. That's called made to measure. Its where you have one stock design and then its custom made to your body. For every M2M suit of a style, the patterns will match, label style will match, pockets will match. Its just the size that is different. I hear indochino does a pretty good job of making affordable M2M suits. For their prices I'd imagine a lot of the process is highly automated.
When you get a bespoke suit made, you walk in and sit down with consultant and you figure out every little detail. He helps you pick a pattern that matches your coloring, label width that matches your body size, number of buttons that match your personality. You end up with a suit that is 100% unique to you.
So think of how conservative it is. Someone older, and more conservative could pull of a double breasted suit jacket where someone younger would look like they are wearing a costume. Where something like a single button jacket would is a bit flashier and would fit someone who is much more out going and confident. There are a lot of variations on the same thing. I can just think of styles that run the scales of traditional vs modern and flashy vs conservative, but with those 2 axises you can do a lot to find something to really accent someones personality and style.
Single buttons have their roots in the single-breasted dinner jacket or tuxedo. If you want your jacket to have an increased level of formality, you'd go with a single button.
Two-button suits are more standard, common for business and every-day suiting. Formal enough for the majority of situations when you'd wear a suit, but not quite "after six" level of formality for an evening event or dinner.
Three-button jackets should be left to casual suits or odd-jackets. Adding more buttons on the single-breasted suit adds an increased level of informality. Works best on casual, seasonal fabrics like seersucker, linen, tweed, corduroy, etc.
Double-breasted jackets have their roots in the military and are often paired with peak lapels, which are more formal than the notched lapels of most suits. So, a double-breasted suit would be definitely on the more formal end.
So, I wouldn't say that buttons are about "personality" as much as it is the situation in which you'll be wearing the suit.
What you described on the bottom is not unique to bespoke, these details can be just as easily adjusted on a made to measure suit.
What's unique about bespoke is that the tailor (technically, the cutter) will make a brand new pattern just for your body, which will be based on a much greater number of measurements. Also, the fitting of a bespoke suit involves multiple fittings (http://www.thesimplyrefined.com/wp-content/uploads/2012/02/B...), using each iteration to ensure a perfect "fit" in accordance with the tailor's vision.
Made to measure suits, on the other hand, involve a single fitting. After the fitting, the suit is made, and can only be altered to the same extent as, say, a standard size suit that you bought at a store.
When you get a bespoke suit made, you walk in and sit down with consultant and you figure out every little detail. He helps you pick a pattern that matches your coloring, label width that matches your body size, number of buttons that match your personality. You end up with a suit that is 100% unique to you.