Vanity plates (or personalized plates) allow you to choose your own plate number
affinity plates (or specialty plates) are a broad category of plates that allow you to show support for a charity, college, team, etc.

https://en.wikipedia.org/wiki/Vanity_plate
https://en.wikipedia.org/wiki/Vehicle_registration_plates_of_the_United_States#Vanity_plates
https://www.dmv.org/pa-pennsylvania/special-license-plates.php
https://www.flhsmv.gov/specialtytags/slpfaq.html
https://www.njeffersonnews.com/news/local_news/want-to-commit-to-a-specialty-alabama-license-plate-now/article_9e586f52-e39a-55d3-b103-80e69b36897f.html