Every periodic chart I ever use says group one is Alkali, and group 2 is Alkaline.
The word "alkali" comes from the Arabic language; ancient Arabian chemists discovered that ashes of certain plants, which they called al-qali, gave water solutions that felt slippery and burned the skin. These ashes contain compounds of Group 1A element that produce alkaline (basic) solutions.
And while I can not find where the IUPAC actually defines Alkali and Alkaline, but both the IUPAC-NIST pooled data clearly use Alkali to define group 1 and Alkaline Earth as group 2.