Close detached binaries were theoretically predicted to evolve into contact by three subtypes of case A binary evolution, cases AD, AR, and AS, which correspond to the formation of contact during dynamic-, thermal-, and nuclear-time-scale mass transfer phases, respectively. It is unclear, however, what is the difference between contact binaries in these subtypes, and whether all of these subtypes can account for the formation of observed W Ursae Majoris (W UMa) binaries. Using Eggleton's stellar evolution code with the non-conservative assumption, I obtained the low-mass contact binaries produced by cases AD, AR, and AS at the moment of contact and their parameter spaces. The results support that the progenitors of low-mass contact binaries are detached binaries with orbital periods shorter than similar to 2-5 d, and their borderlines depend strongly on the primary mass. In addition, the period-colour relations for cases AR and AS can be in better agreement with that for observed W UMa candidates, but case AD shows a significantly worse agreement. Moreover, cases AR and AS can produce a short-period limit (corresponding to a low-mass limit) at almost any age, e.g. from young age (similar to 0.2 Gyr) to old age (similar to 13 Gyr), agreeing with observed W UMa binaries in star clusters, but no such limit occurs for case AD at any age. These results support that cases AR and AS, as opposed to case AD, can lead to W UMa binaries (including young W UMa binaries).