The online/store relationship has gone through a transformation over the past twenty years.
In 2003, you brought in a new customer via e-commerce and that customer migrated over to the store and generally became a good store customer over time.
Not true in 2023.
In 2023, customers have preferences. There are e-commerce customers. There are clearly in-store retail shoppers who embrace that channel, and those customers are a bit less likely to cross-over and buy from e-commerce than they were twenty years ago. There are "hybrid" customers who use each channel for informational/operational purposes.
From a category standpoint, there are differences - and modern customer behavior manifests itself via a category/channel interaction. One retail brand couldn't sell extended sizes in stores - not enough shelf space. Well guess what? Categories with a ton of extended size customers skewed online. Duh! From a marketing standpoint, take advantage of that information. Teach your customers where to buy various categories. Why are you sending emails to extended size customers demanding they shop in your store when you don't carry what that customers wears in your store?
Use category information to modernize your marketing tactics.