If everything is working properly, you can anticipate the wavelength quite well, and indeed, devices very often come out exactly as designed. If things are not working properly, it can be a crapshoot. If something goes wrong, it can be pretty off.
The wavelength is determined largely by the bandgap of the semiconductor used in the active region. It is also dependent on other things with a laser, like the waveguide, but the biggest factor is bandgap. You mention the violet and blue being similar, and that is absolutely true, they are VERY similar. Start with the same substrate, grow a very similar structure, and you can make either wavelength. You "just" (haha, it's not simple) have to decrease the bandgap of the active region (the place the light is emitted) and then tailor the rest of the structure to fit the other wavelength. If you're starting from a violet laser structure and just change the bandgap to emit blue light, that basically screws up several other components of the structure, and you have to adjust the others in order to fit the new device and new wavelength. With LEDs it's much easier, there's much less to have to adjust, but all the pieces have to come together to make a laser diode.
In the violet/blue/green laser diode region, the active region is made of InGaN, indium gallium nitride. Basically, GaN has a higher-energy bandgap that would emit in the UV. Adding indium, which replaces the gallium in the crystal, lowers the bandgap, thereby changing the wavelength of light emitted. In a perfect world, adding indium would be easy, and it is pretty easy to add a little bit of indium, hence making violet lasers is much easier than blue, which require more indium. And even harder are green lasers, which require a LOT of indium. Basically, as you add indium, the size difference between In and Ga atoms creates strain in the material, and sometimes instead of staying "GaN with In evenly interspersed throughout", with too much indium the material would rather become "InN and GaN", instead of "InGaN", as the In and Ga will cluster together with atoms of their own kind. This can actually be a good thing sometimes for some applications, but it's generally not very good for lasers.
So yeah, in the blue end of the spectrum, it is currently possible to grow a laser diode with any wavelength between near-UV (~380nm, I believe) and green (highest reported 531nm). And you somewhat pick what wavelength will come out. Mind you, at the extremes of UV and green, VERY few companies or universities can make those, because they're very hard to make.
In the red end of the spectrum, some things are easier, but some things are harder. They worry a lot more about something called lattice-matching, and have different variables spaces to work in. That is to say, some things that are adjustable in the red region are not adjustable in the blue region, and vice-versa.
Another little detail is that the wavelength never comes out EXACT. Hence diodes always having the +/- 5nm, or even +/- 10nm, rating on the wavelength. There is just variability, and you can't get that precise. If you do everything right, the diodes will average a certain wavelength, but even within a single wafer, the wavelengths will vary from different places on the wafer.
Make sense?