IMO, that's a distinction without a difference. Viral is viral, whether there is agency involved or not. It's about people communicating and behavior spreading through a social network.
The downside of forcing virality is reflected in additional metrics like retention rates and engagement.
The difference is in acknowledging that the people spreading the message do that out of their own will - not because they have been contaminated by the meme. In other the 'spreadable' metaphor focuses the thinking on why people want to spread the message, what they get out of it, makes the message author to concentrate on cooperating with the spreaders - instead of trying to contaminate them.
The downside of forcing virality is reflected in additional metrics like retention rates and engagement.