Historically Siam was part of Indochina; a confluence. Like the rivers.

Conflating the South East as a part of the South or East Asia because it has both names is as someone saying Texas is not West or Eastern US while being in the "middle" geographically.

South East Asia is markedly different to South or East Asia. It's a melting pot of both cultures + Melayu and other groups. South East Asians that descended from South Asia (Ex: Malaysian/Singaporean with Indian ancestry) mostly identifies as South East Asians. Same with people who have East Asian ancestry (Ex: mainly Chinese ancestry across SEA). The immigration happened hundreds or even thousands of years ago and some are very distinct groups and cultures from their origins due to time and separation.