In short, Regulation A (Reg A) and Regulation A+ (Reg A+) are the exact same law and both terms can be used interchangeably.
Historically, Regulation A was the term originally adopted by the SEC under Section 3(b) of the Securities Act in 1936. At this time in history, there was no “Regulation A+” terminology being used. Beginning in 2012 when the Jumpstart Our Business Startups (JOBS) Act was signed into law by President Barack Obama, the SEC started using the terms “Regulation A+” and “Reg A+” as a way to differentiate the new version of Regulation A law from the original version dating back to 1936.
Most notably with the passing of the JOBS act, the maximum offering amount was increased from a limit of $5M up to $50M… and eventually up to $75M for Tier 2 Reg A offerings (Tier 1 Reg A offerings capped at $20M). More on the difference between a Tier 1 vs Tier 2 Reg A can be found here.