IM?s are typically very small and does not use much data at all. Even if you are heavy messages user, you are not likely to put a dent into your data by sending messages. However, images and files are another story. For messages though, it will take 1024 characters to make 1kb?. As you can see, you can send a lot of messages before you start to have a negative impact on your data. This is also to assume that all of your data usage is on the cellular network. If you are connected to wifi? and connected to the Internet that way, then you are not using cellular data, and therefore doesn’t count against your cellular data.
This is to assume that both parties are using the same IM service. At the very least, this will likely be RCS? which as noted above uses data. RCS is standard with all Android phones, and iPhones communicating with Android phones. RCS is more capable than SMS?, and with SMS, you might be charged international rates if you send an SMS to a phone number outside of your country. Always be sure that RCS is enabled before sending a lot of messages.
If the person you are sending an IM to is using a basic phone, KaiOS phone, or a Graphene OS? device, you would be using SMS. The recipient’s device simply can not support RCS. If you have an iPhone, and communicating to another person with an iPhone, than all of your messages will be iMessage which is much like RCS, so I would expect that there will be no difference.