How does the Microsoft tablediff utility work?
I'm not aware of authoritative documentation of the fact that the current version of the tablediff utility uses a checksum to identify data differences. However, I was able to verify this by capturing the queries executed by the utility using a sql_batch_completed event trace. The trace showed a query is run against each table, returning only the primary key value(s) along with the T-SQL BINARY_CHECKSUM over all table columns. 

This is the T-SQL script I ran on my local SQL instance to the create tables and trace:

USE tempdb;
DROP TABLE IF EXISTS dbo.table1;
DROP TABLE IF EXISTS dbo.table2;
CREATE TABLE dbo.Table1(Col1 int NOT NULL CONSTRAINT PK_Table1 PRIMARY KEY, Col2 int);
CREATE TABLE dbo.Table2(Col1 int NOT NULL CONSTRAINT PK_Table2 PRIMARY KEY, Col2 int);
INSERT INTO dbo.Table1 VALUES
      (1, 1)
    , (2, 2)
    , (3, 3);
INSERT INTO dbo.Table2 VALUES
      (1, 1)
    , (2, 0)
    , (4, 4);


While viewing the trace in SSMS (Object Explorer: right-click Management-->Extended Events-->Sessions-->sql_batch_completed and select Watch Live Data), I ran this from the command prompt:

"C:\Program Files\Microsoft SQL Server\140\COM\tablediff" -sourceserver "." -sourcedatabase "tempdb" -sourceschema "dbo" -sourcetable "Table1" -destinationserver "." -destinationschema "dbo" -destinationdatabase "tempdb" -destinationtable "Table2"


These were the relevant queries executed by tablediff:

SELECT [dbo].[table1].[col1],BINARY_CHECKSUM([dbo].[table1].[col1],[dbo].[table1].[col2],[dbo].[table1].[col3]) as MShash_54267293 FROM [dbo].[table1] WITH (READUNCOMMITTED) ORDER BY [dbo].[table1].[col1]

SELECT [dbo].[table2].[col1],BINARY_CHECKSUM([dbo].[table2].[col1],[dbo].[table2].[col2],[dbo].[table2].[col3]) as MShash_54267293 FROM [dbo].[table2] WITH (READUNCOMMITTED) ORDER BY [dbo].[table2].[col1]