Yes, your Snapchat score mainly goes up when you send and receive snaps, not regular text chats. So if you are only chatting with someone in the chat section, your Snap score usually will not change. Posting stories can sometimes affect it a little too, but chats alone are not the main factor. Snapchat does not fully explain their scoring system publicly, so some small changes can feel random at times.
I noticed my score increased much faster when I exchanged photo snaps daily with friends, while normal chats barely made any difference.
I cannot confirm every hidden detail of Snapchat’s algorithm because Snapchat has never shared the full formula publicly, so for very technical details, checking Snapchat support or community discussions may help more.