Check out example codes for "sql update from two different database". It will help you in understanding the concepts better.
Code Example 1
update table_name1 set column_name = T2.column_name from database_name.dbo.table_name2 as T2 where table_name1.ID = T2.ID
Code Example 2
update table1 set col2 = T2.col2 from DataBaseName.dbo.table1 as T2 where table1.ID = T2.ID and table1.col2 is null
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