Vyvyan Basterd
Adventurer
Erm, not quite true. When 2e was released 1e was still in print and Basic was either still in print or had just gone out of it. 1e and 2e overlapped by about 2 years, if memory serves: TSR was in essence competing with itself.
There was no overlap between 1st & 2nd edition AD&D. The final products of the BECMI line, Immortals and the Rules Cyclopedia were published in 1991, so there a two-year overlap between 2nd edition AD&D and BECMI/RC D&D. TSR had been competing with itself for 14 years by 1991 with the split between D&D and AD&D.