To me, the big difference is that if you do just online work, you're essentially defeating the purpose of going to a place of work. You can do it in the comfort of your own home, work your own hours, and so on. With a business offline, or in person work, you don't usually get to pick your hours, or pick the type of work you want to do.
Now if you mean offline in the sense this business doesn't have a website, that's one thing. Some businesses can flourish without a web presence. As long as they have brand recognition, they should be fine. For example, lets say McDonalds stopped advertising. I am willing to bet that those ads didn't really do much, as people flock to McDonalds on the daily. I doubt they did so because of advertising. It's all word of mouth and the fact there's a McDonalds on every street these days.