So this seems to be a shared universe game, is the a "canon" order to the games? And if possible can I get either likes to the other ones, or an easy search term?
They reference each other but there's no order. It's mostly just a sort of friendly cooperation by devs where they reference each others' games, mostly for fun. The other games are here if you search for the title.
There's a significant mutual shoutout between this game and Leap of Faith; Jaye appears for a bit in that game where the main character gets to have a chat with her, and she gets a selfie with the rock star in that game that shows up in CS. There's another connection to Summer Scent; doing the Jaye route will have the characters from that game show up in CS, while Jaye meets them for dinner in SS; there's also the running joke about the "naughty French captain" in CS, since the dev of SS is "Naughty Captain" and is French. There is a tiny crossover with Artemis in a scene where Amanda is chatting online with someone who turns out to be from that game.
There are also other crossovers in those other games that extend the universe further. Leap of Faith crosses over a lot with Artemis, with a lot of jokes that both games use the same base model for their main characters. LoF also crosses over with a new game by the same dev, u4ia, since one love interest in that game is a character in LoF. LoF also crosses over with some others; there's a cameo by a character from STWA Unbroken, and the end scene has a concert with tons of crossover guests, but that's more of a funny than a canonical shared universe. There are no doubt more.
All of the ones I've mentioned are good games, worth playing. My one warning if you go into them knowing nothing is that Leap of Faith is spectacular, but it's a game that is absolutely an emotional gut punch; if you are feeling fragile, leave it for later. The game is best if you don't spoil it at all, but it confronts severe mental health issues and doesn't pull punches. You'll have a sense by the end of chapter 1 if you'll be okay, but chapter 6 (of 8) in particular is crazy dark from beginning to end, so consider not playing it if you're struggling. That said, it's a great game, maybe my favourite (though CS gives it a good run honestly); it's genuinely a great story that is good at using comic relief and sex to relieve the heaviness some (indeed, one of the main characters even meta-references that) and is the best "novel" as literature I've seen in AVNs -- definitely some dropped plot lines and things that I wish were a bit cleaner, and it's a good example of the danger of too many romance paths in one story. Honestly, I wish there was a less NC17 version I could get friends who don't do AVNs to play because I really want to talk with someone in real life about that game.