The reason to keep the versions straight is that three of them govern three things in a single retiree's finances, and each is fixed by a different document.
Federal tax figures run on chained CPI. Section 1(f)(3)(A) sets the annual adjustment as the percentage by which "the C-CPI-U for the preceding calendar year" exceeds "the CPI for calendar year 2016," and section 1(f)(6)(B) defines the annual value as "the average of the C-CPI-U as of the close of the 12-month period ending on August 31 of such calendar year." That switch was made by section 11002 of the 2017 tax act, it reached essentially every indexed figure in the Code at once, and its effective-date provision says only that the amendments "shall apply to taxable years beginning after December 31, 2017," with no termination date attached. So chained indexing has been permanent since enactment rather than something later legislation had to preserve. The 2016 handover is bridged by a splice factor in section 1(f)(3)(B), which divides the chained index for 2016 by the traditional index for 2016, so the change of series did not itself reset any threshold.
The Social Security increase runs on CPI-W, and the reason is worth stating precisely because it is usually stated wrongly. The statute at 42 USC 415(i) refers only to "the Consumer Price Index ... as prepared by the Department of Labor" and names no version. The Social Security Administration explains the choice in its own annual determination: "At the time the Act was amended to provide automatic cost-of-living increases starting in 1975, only one CPI existed, namely the index now referred to as CPI for Urban Wage Earners and Clerical Workers (CPI-W). Although the Bureau of Labor Statistics has since developed other CPIs, we follow precedent by continuing to use the CPI-W." That is an agency practice resting on history, not a statutory command, which is a meaningful distinction in any argument about changing the measure.
Series I savings bond rates run on a third variant. Treasury states that it bases the inflation component "on changes in the non-seasonally adjusted Consumer Price Index for all Urban Consumers (CPI-U) for all items, including food and energy." So it is the unadjusted, all-items series, which is neither the chained measure the tax tables use nor the wage-earner measure Social Security uses.
Two features of how the numbers are produced matter more than they sound. The first is seasonal adjustment. The same month has both a seasonally adjusted and an unadjusted reading, month-over-month commentary conventionally uses the adjusted series while year-over-year comparisons and formula applications such as the savings bond rate use the unadjusted one, and a reader comparing two reports of "inflation last month" may simply be comparing the two versions. The second is revision. Chained CPI is uniquely subject to later revision, because its expenditure weights are estimated when first published and firmed up afterward, and section 1(f)(6)(A) locks the tax figures to "the latest values so published as of the date on which such Bureau publishes the initial value ... for the month of August for the preceding calendar year." The tables are therefore built on an unrevised snapshot and are never recomputed when the index is later corrected. The other series in this entry carry no such asymmetry.
Two further points about construction explain much of the confusion around the index. The first is how owner-occupied housing is handled. Shelter enters through rent and through owners' equivalent rent, an estimate of what an owner-occupied home would rent for. The price of a house does not enter, and the reason is that a house is treated as a capital asset rather than as something consumed: its price reflects both an investment value, which a cost-of-living index sets out to ignore, and the shelter it supplies, which is the part the index is after. Owners' equivalent rent is the attempt to isolate the second. The change was announced in 1981 and phased in one series at a time rather than all at once, reaching CPI-U with the data for January 1983 and CPI-W two years later. Before it, the measurement turned partly on mortgage interest rates, so a rise in rates by itself pushed measured inflation up. This is the best available explanation of why the index can look wrong to someone shopping for a first home in a rising market: what they are about to pay for the asset is not what the index is measuring.
The second is that the family includes a member built for older households, and it is not the one the benefit formula uses. In a 2019 Federal Register request for comment on the consumer inflation measures produced by federal statistical agencies, the Office of Management and Budget described an experimental Consumer Price Index for the Elderly, written CPI-E, which "uses the same price surveys and formulas as the CPI-U and CPI-W, but uses expenditure weights for households with a reference person or spouse aged 62 years or older," and stated that it "is an experimental index and is not currently used for official purposes." Legislation to substitute it for CPI-W is introduced in Congress after Congress, and anyone relying on its status should confirm it at the Bureau, which publishes the series.