Who has invented more words, men or women?

words are very rarely “invented,” at least not in any way you seem to mean or we can understand or have clear records of. i suspect more words are probably first recorded in writings by men, but that’s because more writings by men have been published & preserved, for reasons i’m sure you can guess. there’s some evidence that women actually lead linguistic change, probably because women have historically been the ones who teach the next generation to speak.

by the way, your girlfriend is right. at least in the us, “tip” and “gratuity” mean the same thing, and you should always tip your server

Why did u assume men had made more? It's generally not advised to make statements like that without knowing. But either way, hard to know, words aren't often invented they usually develop and merge and stuff from preexisting things or older things which if u trace it back would be just made up but we have no clue who by cos nobody does. Sometimes words are invented like in science and writers and stuff, like Shakespeare made a bunch and new words are made very often via preexisting morphemes by biologists and doctors and the like. And contrary to popular belief ratio of women to men in science is only slightly leaning to the male side by about 7 percent, so we can't say men just because of something like that it's not really enough.

So in conclusion, don't make factual statements that u have no remote proof of, and we have no idea. If this sounds angry or critical it's not I'm just tired and don't have the energy to soften my tone.

typically the etymology of a word is a terrible way to argue about what it means right now

a gratuity and a tip are the same thing. In the US always tip your server.

Whether men or women innovate more language might be an interesting question, but I don't know that we have any hard evidence about who has done so historically.

Whether men or women invented more words is completely irrelevant to any argument you might be having about what a word means, that's a false appeal to authority. Even if men have innovated more vocabulary than women, that doesn't mean the random dudes at the foodbank know what a gratuity is. A gratuity and a tip are identical in American English in the context of a restaurant, and there's no historical or etymological argument about what these words used to mean that will change that. In fact, tips were also used as a way to say thank you in the past, but for decades it has been extremely rude not to tip your server because of the way the tipping system works. Waiters get paid less than minimum wage because they are expected to get most of thei wage from tips. This is true whether the receipt says gratuity or tip. The reason tipping is mandatory is this system, so no matter what they call it on the receipt, you should tip.

https://www.smithsonianmag.com/smart-news/teenage-girls-have-been-revolutionizing-language-16th-century-180956216/

You might find this interesting. While not the same thing as "inventing words", necessarily, (there are lots of other ways new words enter our vocabularies/language...) young women have historically been driving some serious linguistic change. (One of my favorite examples is "hath" and "doth" becoming "has" and "does", it's mentioned in this article but I also learned about it at Planet Word in DC, just while we're speaking about the importance of educating ourselves before making assumptions)