There are a number of coins within the classic US commemorative coin series that were issued for one purpose, but some collectors think they mark an entirely different event.
Following are several for which I've had to personally redirect one or more collectors about the purpose of a particulare coin.
Note All instances of bolded text in the bill/Act text below was added by me for emphasis. 1918 Illinois Statehood Centennial Half Dollar

The prominent portrait of Abraham Lincoln is enough to make some collectors think the coin honors the 16th US President vs. the State of Illinois. Lincoln's close association with Illinois - much of his pre-presidency professional/political life was lived in Illinois - was the driver behind the inclusion of his image as part of the coin's designs, but the coin was most definitely issued on behalf of the State and not Lincoln himself. The coin's enacting legislation clearly states the coins were to be struck "in commemoration of the
one hundredth anniversary of the admission of the State of Illinois into the Union." (Public Law, 65-163)
1927 Battle of Bennington / Vermont Independence Sesquicentennial Half Dollar

The Benningon / Vermont half dollar is one of several coins of the classic era that is often considered a Statehood Anniversary coin vs. its true purpose. The Benningon / Vermont half dollar was issued "in commemoration of the one hundred and fiftieth anniversary of the Battle of Bennington and the
independence of Vermont." (Public Law 68-452) In 1775, the year being commemorated by the coin, Vermont was its own Republic, it did not become a State in the Union until March 4, 1791.
1928 Hawaiian (European) Discovery Sesquicentennial Half Dollar

More than once I've heard a collector talk about the 1928 "Hawaii Statehood" half dollar. Clearly, such collectors are not students of history! Hawaii did not become a US State until August 21, 1959, so a 1928 half dollar wasn't connected to any Hawaii Statehood celebration. The 1928 coin was struck "in commemoration of
the one hundred and fiftieth anniversary of the discovery of the Hawaiian Islands by Captain James Cook, and for the purpose of aiding in establishing a Captain James Cook memorial collection in the archives of the Territory of Hawaii." (Public Law, 70-98) No statehood anniversary in site!
1934 Maryland Tercentenary Half Dollar

I once sat across a lunch table from a fellow collector at a coin show/convention and listened to him describe his new Maryland half dollar as a coin that celebrated Maryland's Statehood. I felt compelled to point out that the coin was marking a 300th anniversary (i.e., a tercentenary) for a very different event and that there weren't any states in 1634 - the proposed coin was struck "in commemoration of the three hundredth anniversary of the
founding of the Province of Maryland." (Public Law, 73-215) At that show, the collector in question got a new coin and an education - always a good pairing IMO.
1934-38 Texas Independence Centennial Half Dollar

The Texas half dollar is another coin that recognizes an independent republic but is often thought of as a Statehood Anniversary coin - I've seen the mistake on web sites as well as hearing it from collectors. Texas declared its independence from Mexico on March 2, 1836; it operated as the independent "Republic of Texas" until it became a State on December 29, 1845 (the Republic formally transferred its power to the State of Texas on February 19, 1846). The coin was struck "in commemoration of the one hundredth anniversary in 1936 of the
independence of Texas, and of the noble and heroic sacrifices of her pioneers, whose revered memory has been an inspiration to her sons and daughters during the past century. (Public Law, 73-59) It was not issued as a Statehood Anniversary coin!
1935 Bridgeport, CT Centennial

Several collectors (and one dealer!) I've encountered, believed the 1936 Bridgeport, CT Centennial half dollar marked the 100th anniversary of the founding of Bridgeport. In reality, Bridgeport traces its foundational roots to a small of group of settlers who moved into the area in the 1660s. The coin was issued "in commemoration of the one-hundredth anniversary of the
incorporation of Bridgeport, Connecticut, as a city." (Public Law,74-596) In other words, the coin marks an 1836 event, not one from the 1660s.
1936 Wisconsin Territorial Centennial Half Dollar

The common name for the 1936 Wisconsin Territorial Centennial half dollar is the "Wisconsin." With a nickname like that, it's not much of a surprise that some collectors think of the half dollar as one that marks the State of Wisconsin''s centennial. Wisconsin was established as a Territory on July 3, 1836 - it was not a State in 1836. Wisconsin attained Statehood on May 29, 1848. The half dollar's enacting legislation states that the coins were to be struck "in commemoration of the one-hundredth anniversary of the establishment of the
Territorial Government of Wisconsin, and to assist in the celebration of the Wisconsin Centennial during the year of 1936." (Public Law, 74-593) (Wisconsin tried for a Statehood coin in 1948, but it didn't pass Congress. Check out my What If? story on it if you'd like to learn more.)
There are likely others, but those are ones I have personal experience with. What can you add from your experiences?
You can find my previous posts on each of the coins discussed above here:
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Commems Collection (There are multiple on each.)