update record from two diffrent database code example

Example 1: sql update from two different database

update table_name1
set column_name = T2.column_name
from database_name.dbo.table_name2 as T2
  where table_name1.ID = T2.ID

Example 2: sql update from two different database

update table1
set col2 = T2.col2
from DataBaseName.dbo.table1 as T2
  where table1.ID = T2.ID and
        table1.col2 is null