Are elements in the same column down members of the same period or group?
Elements in the same vertical column are members of the same GROUP.
And elements in the same horizontal row are members of the same PERIOD.
These designations are important, because the modern Periodic Table's preoccupation with rows and columns, Groups and Periods, is a reflection of electronic structure. Members of the same Group have the same valence electronic configuration to a first approximation, and thus, again to a first approximation, have the same chemistry.