First of all, 'Evette & Schaeffer' model clarinets are not the same as 'Evettes.' When this designation was used, the Evette was Buffet's student/low-end intermediate wood instrument. The Evette & Schaeffer model was Buffet's high-end intermediate model. (Evette and Schaeffer were two partners who purchased the Buffet company in the early part of the 20th century but retained the Buffet name.) [See the clarinetperfection link below: Buffet factory was bought in 1885 by two men, whose last names were Evette and Schaeffer. From Annette: Their complete names: Paul Evette and Ernest Schaeffer.]
Both models appear to have been around for a long time. I have an early Evette & Schaeffer whose keywork is quite similar in style to the keywork on a professional Buffet instrument from 1936 that a friend of mine owns. Buffet made the model until 1981 or 82 (with significant design changes over the years) when they changed the designation to the E13. All the evidence I have seen indicates that these instruments were always made in the main Buffet factory. The last series was the K-series. It began around 1953 according to the Boosey & Hawkes web site.
As far as I have been able to determine, the (wooden) Evette model dates back about as far as the E&S and these instruments were also made until 1982 -- in France (possibly not all at the main Buffet factory and possibly not all by Buffet) until the late 70's, then in Germany until 1982 when they were renamed the E11. The last (wooden) Evette series was the D-series which began in 1963, according to the B&H site.
In short, the evidence I have seen suggests the following 'equivalences':
Plastic Evette became the B12.
Wooden Evette became the E11.
Evette Master Model became the E12.
Evette & Schaeffer became the E13.
1960 ad:
There was also an Evette & Schaeffer Master Model. There is alot of folk lore surrounding these clarinets as Buffet does not disclose much information about them these days. One popular tale is that the E&S Master Models (another version involves the Evette Master Models) were actually R13's that had failed their final inspection because of some minor imperfection such as a blemish in plating or unattractive wood. However, there are some subtle but definite differences between the E&S Master Model and R13's from the same time period. (I have a couple of each.) On the E&S, the bell is a little longer and the stock barrel a little shorter. Furthermore, there are some differences in the keywork. The most notable is the sliver key on the lower joint. On the E&S, the distance between the two posts for this key is several millimeters longer than the R13. Also there are differences in the design of the lower joint where the right-hand cluster of keys is located. To my eyes, the master model is much more nearly identical to the 'standard' E&S (I don't see any difference) than it is to the R13.