A few key concepts associated with groups and networks really clarify the differences.
Groups
Unity
Value
Closed
Limits
Distributive
Unequal
Networks
Connections
Diversity
Autonomy
Open
Distributed
Equal

Connectivism is about networked learning. This doesn't mean that groups won't form within networks. It just means that connective learning in it's most powerful sense has the characteristics on the right side of this concept map. Those characteristics are what differentiates groups from networks and connectivism from other learning theories.
Just one question...
I'm grappling with the notion that networks are like ecosystems. When I think of an ecosystem, I think of critical dependencies whereby the ecosystem fails when one component fails. Yet in a complex network, a node could theoretically disappear without causing major impact to the network. Again, I'm getting caught up in metaphors when I should be thrilled that all of this is starting to make a lot more sense to me.