Detailed chemical and structural studies for the tetragonal and orthorhombic phases of Tl2Ba2CuO6 are presented. We have shown, for the first time, that these two phases have different chemical compositions; a larger amount of Cu substitutes for Tl and the amount of excess oxygen is less for the tetragonal phase. It is also found that the microscopic environments around Cu in the CuO2 plane are different for the two phases. This leads to the fact that the structural difference, on both macroscopic and microscopic scales, is not of primary significance for the range of superconducting behaviors from normal metals to over-85 K superconductors. The key factor responsible for the wide ranges of T(c)-variation in these compounds seems to be the change in carrier concentration.