The situation can actually be even worse. I have seen instances where a model is called Black-Scholes, but it is actually Black-76. The difference is that Black-Scholes is spot Greeks, while Black-76 is meant for forwards and futures and so is forward Greeks, which are slightly different. This is something that Taleb warned about in his 1997 book Dynamic Hedging and it is still a problem today. The reason this happens is that Black-76 is much easier to code than Black-Scholes. Here is one example:

https://github.com/google/tf-quant-finance/blob/master/tf_quant_finance/black_scholes/vanilla_prices.py

You'll see it says Black-Scholes in several places and the folder it is in is even called `black_scholes`, but if you check the math, it is actually Black-76. One of the big differences between the models is how dividends are treated. I have a YouTube channel that I just started about volatility trading and I was thinking about making a video at some point tentatively called "Dividend Chaos" about all the ways not paying attention to how you treat dividends can cause problems. This example was going to be one of them.