Here is the exact estimated figures by the CSO (Central Statistics Office of Afghanistan) about the Urban and Metropolitan area's populations as of 1387 (2008/2009), taken from CSO Statistical Yearbook 2008/2009:
Kabul: Rural (599,800), Urban (2,850,000), Total (3,449,800)
So the Urban population is the same Kabul city's population, and the Total population is the Metropolitan area's population. Britannica has also considered the Urban population figure as Kabul city's population, and that was based on 2006 (1385) population estimates of the CSO.
To obtain the copy of the CSO Statistical Yearbook 2008/2009, go the CSO's website (ttp://www.cso.gov.af/index.html) and on the left bar, there is a link to the Statistical Yearbook. Or let me give you the direct link to the zip downloadable folder Here. You will see the PDF copy-image of the Population chapter in the sub-folders.