The Very Large Array has been used to obtain ~3'' resolution observations on the 44 GHz 7_0 -> 6_1A+ transition of CH_3OH (methanol) in the Sgr B2 massive star-forming complex. A total of 18 compact regions showing maser emission are found, which are spread over a 2.1 pc * 4.3 pc ( alpha * delta ) region. Many of these are offset far from known molecular cores and ultracompact HII regions and may trace the interaction region of a cloud-cloud collision. There is no spatial coincidence between 44 GHz and 6.7 GHz CH_3OH masers in this region, as expected because the pumping mechanisms for these two transitions are different. Isotropic maser luminosities range between 1*10^-6 and 2.1*10^-5 L_o. In addition, 17 regions with broad-linewidth quasi-thermal 44 GHz CH_3OH emission are identified, many of which are close to known molecular hot cores, in particular those associated with the Sgr B2(N) and Sgr B2(M) continuum sources. In Sgr B2(N), quasi-thermal emission appears to be associated with two 10^'' diameter ionized shells. These ionized shells may have swept up and shocked molecular material as they expanded. Also, a quasi-thermal core is observed to be coincident with a source of continuum emission from dust and emission from more complex species. In Sgr B2(M), CH_3OH quasi-thermal emission arises predominately from the western portion of this region. The CH_3OH fractional abundance in most of the quasi-thermal cores appears to be quite high at ~10^-6. It is argued that grain-surface chemistry is responsible for this high abundance.