The type numbers differentiated carbs manufactured for specific applications. For example, 27 was for a 1600 Giulia GTV/Duetto while 32 was for a 1750 and 18 was for a Lotus Twincam. Most of this had to do with the calibrated components provided by Weber (including all jets, venturis, but also the rods that determine the pump stroke) and also altered the number and position of the progression holes, which is a major factor when adapting carbs to a specific application.
Not all variations are easily transferred to other applications; for example the types 23 and 26 were a matched pair intended for the Renault 8 Gordini on which the installation was very tight. The throttle shaft ends are a very compact arrangement that could not be used on an Alfa. Similarly the types 34 and 35 were another matched pair designed for the Sunbeam Rapier H120; they are missing a breather hole in the float chamber. They are said to adapt very poorly to other applications.
Around 1980 Weber introduced the type 151 40DCOE (and type 152 45DCOE) with plastic floats; these are regarded as a great evolution and are still available today. Production was transferred to Spain in the early 90s, which does not alter their desirability. They had initial problems but after 30 years I would believe the bugs have been worked out. These are generic aftermarket carbs, not designed for a specific application.
Alfa made cars with twin Weber carbs until the early 90s. At some point they switched to the DCOM, a variation on the DCOE theme that included a diaphragm acceleration pump and other emission features. These are not regarded as performance carbs and are better left to their intended applications.
There have been numerous copies over the years; we all know the slightly different Dellorto DHLA and Solex PHH as well as the Japanese Mikuni Solex. At some point Shankle was offering Japanese SK clones of the DCOE, which used most if not all of the Weber calibrated parts. These are still made in Japan under the OER name.
Empi markets Chinese copies of various Weber carburators. I haven't seen Empi DCOE clones, but some are marketed as FAJS and GOWE. From what I understand these are best left alone.