During my time here on CCF, I've regularly referred to medals, tokens and other items of exonumia that are directly connected to a given coin via the same sponsor organization as "cousins."
Of course, big events are the subject of many independent, third-party medals, etc. A collector can spend a lifetime, for example, trying to track down an example of each of the numismatic items produced for the 1893 World's Columbian Exposition. Such "independent" items are clearly related to the legal t ender coins, so the term "cousin" seems still to apply, but I like to call them "third cousins" to better represent their place in the coin's "extended f amily."
Here's such a "third cousin" for the 1936 Providence, Rhode Island Tercentenary Half Dollar - a privately-struck brass medal with a proof-like finish that features designs similar in theme to the half dollar but without an official link to the Rhode Island and Providence Plantations Tercentenary Committee, Inc. - the coin's sponsor. I added it to my collection because of its design theme similarities - I thought it would make for an interesting story!
The medal, at 31.8 mm in diameter. is just slightly larger than a US half dollar (30.6 mm). It has a smooth edge and was struck using the traditional medal alignment (i.e., obverse and reverse oriented in same direction).
1936 Rhode Island Tercentenary Commemorative Medal

The medal's obverse presents a Roger Williams landing scene - Roger Williams is considered the founder of Rhode Island. The depiction of Williams coming ashore and being greeted by local Native Americans is presented in a realistic manner vs. the half dollar's highly stylized depiction.
I'd bet a nickel, the medal's obverse is based on the following illustration from the 1880s:
Roger Williams Landing at Narragansett (future Providence)
(Image Credit: Stephens, Alexander. A Comprehensive and Popular History of the United States. 1882. Public Domain.)As does the coin, the medal's reverse design uses an anchor theme derived from the historic Rhode Island Seal. The medal features a fouled anchor (i.e., an anchor with its cable wrapped around it) vs. the coin's free anchor; above the anchor is the inscription "HOPE" which has been part of the Rhode Island Seal since the 1640s. Rhode Island's anniversary dates "1636" and "1936" flank the anchor. (A fouled anchor was featured on early RI Seals, but is not used on the current Seal.)
1936 Providence, RI Tercentenary Half Dollar

The medal is fairly common in the marketplace - a sign it was likely produced in large numbers - and you should be able to find a nice example for $10 or less. It appears that the company that produced the medal shown, also produced other versions that include the same anchor design paired with a different opposite side die; I've seen a South Kingston, RI piece, an Old Stone Bank piece and a Brown & Sharp Manufacturing Company piece. There are likely others, but as I don't collect them, I have not tried to compile a comprehensive list.
For more of my topics on commemorative coins and medals, including more on the history of the Rhode Island Tercentenary half dollar, see:
Commems Collection.
For more on the Rhode Island Seal, check out:
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Official Seals On Classic US Commemoratives - Part V