In October 2018 I paid $140 for NHL.TV, which is the streaming package that lets you watch out-of-market hockey games on your TV using a streaming box like a Roku or Apple TV, or on your computer. This price got me the entire 2018-2019 season.
The NHL Network is the cable channel that is available from most cable companies and a small number of streaming services (DirecTV Now and Sling TV). They have a lot of hockey shows and a smattering of hockey games throughout the season. In the US, NHL Network also broadcasts some international tournaments like the World Hockey Championship.
An NHL.TV subscription does not include NHL Network. It sure would be nice if it did. Sling TV has affordable options for getting NHL Network, but overall Sling TV (to me at least) is not a very appealing streaming service. And Directv Now only offers NHL Network in their most expensive bundles of channels, so it's not very affordable.
My opinion: for now it's hard to "cut the cord" and get NHL Network in any way that really makes sense. I'm hoping that the more appealing streaming services like PlayStation Vue and YouTube TV eventually add the NHL Network.