The difference is that you were not aware of how interested in LinkedIn the contact was, and you were not aware you were ALSO inviting her to join LinkedIn
The difference is that sending a request to someone within the social network to form a connection in that social network is different than sending an invite to someone's separate social network (email), which encourages them to join a whole new social network are two separate actions, and to represent one while doing the other is a bait-and-switch. This is a problem because they have separate social and cultural expectations, so you may feel comfortable doing one and not the other.
The difference is that you were not aware of how interested in LinkedIn the contact was, and you were not aware you were ALSO inviting her to join LinkedIn