Notes on Different Measures of the Consumer Price Index.

The Consumer Price Index (CPI) is the broadest inflation measure published by U.S. Government, through the Bureau of Labor Statistics (BLS), Department of Labor:

The CPI-U (Consumer Price Index for All Urban Consumers) is the monthly headline inflation number (seasonally adjusted) and is the broadest in its coverage, representing the buying patterns of all urban consumers. Its standard measure is not seasonally adjusted, and it never is revised on that basis except for outright errors,  

The CPI-W (CPI for Urban Wage Earners and Clerical Workers) covers the more-narrow universe of urban wage earners and clerical workers and is used in determining cost of living adjustments in government programs such as Social Security. Otherwise its background is the same as the CPI-U. 

The C-CPI-U (Chain-Weighted CPI-U) is an experimental measure, where the weighting of components is fully substitution based. It generally shows lower annual inflation rate than the CPI-U and CPI-W. The latter two measures once had fixed weightings — so as to measure the cost of living of maintaining a constant standard of living — but now are quasi-substitution-based. 

The ShadowStats Alternative CPI-U measures are attempts at adjusting reported CPI-U inflation for the impact of methodological change of recent decades designed to move the concept of the CPI away from being a measure of the cost of living needed to maintain a constant standard of living.