The three funds mentioned are different in several ways. From the "Strategy and Policy" information for each fund at the Vanguard website:
FTSE ex US: VFWIX: The fund employs a “passive management”—or indexing—investment approach designed to track the performance of the FTSE All-World ex US Index. The index includes approximately 2,200 stocks of companies in 47 countries, from both developed and emerging markets around the world. The fund invests in a broadly diversified sampling of stocks in the index that approximates the index’s key risk factors and characteristics.
TMI: VTMGX: The fund invests in stocks included in the Morgan Stanley Capital International® (MSCI®) Europe, Australasia, Far East (EAFE®) Index, which is made up of common stocks of companies located in Europe, Australia, Asia, and the Far East. The fund uses statistical methods to sample the index, aiming to closely track its investment performance.
Total International: VGTSX: The fund employs a “passive management”—or indexing—investment approach. The fund seeks to track the performance of the Total International Composite Index by investing in three other Vanguard funds—Vanguard European Stock Index Fund, Vanguard Pacific Stock Index Fund, and Vanguard Emerging Markets Stock Index Fund. These other funds seek to track the MSCI Europe Index, the MSCI Pacific Index, and the MSCI Emerging Markets Index, which together make up the Total International Composite Index. The fund allocates all, or substantially all, of its assets among the European Stock Index Fund, the Pacific Stock Index Fund, and the Emerging Markets Stock Index Fund, based on the market capitalization of European, Pacific, and emerging markets stocks in the Total International Composite Index
FTSE will get you the foreign tax credit which you won't get with a fund of funds like VGTSX. As already mentioned TI lacks Canada.
FWIW personally I own the ETF version of FTSE ex US in a taxable account as the bulk of my International allocation.
DD