In a Youtube comment (I know right) someone told Matt Coleville, "I used to think you were a God-Tier DM, but after watching your game you're just a really good Storyteller." The statement led to a lot of confusion to people when the comment was shared (sans name) on twitter, which is where I found it. In unpacking it the closest some people could come to explaining their - similar - view is that DMs like Matt Mercer spoiled them for what a God Tier DM is.
Now, to be clear, there is absolutely nothing wrong with liking Matt Mercer's DMing style over Matt Coleville. However, if you are expecting all DMs, GMs, and Storytellers to run their game like Matt Mercer that is unfair to whomever is running the game at your table - especially if that person is you.
The idea of good Storyteller and good DM are so intertwined that the entire World of Darkness series (Vampire, Werewolf, Mage, Demon, Changeling, etc) calls the person who runs the game the Storyteller. But while the concepts are similar, a DM has different responsibilities than a Storyteller. And I don't mean Storyteller as the GM for a World of Darkness Game.
A storyteller's responsibility is to weave a tale that entertains the audience it is presented for. That is their sole job. If a story grabs you, wraps you in its world, and hangs you on the peaks and valleys of its plot, then it is likely being given by a good storyteller.
A good storyteller knows what to focus on with a telling, what aspects to put into questions, and how to play to the drama of a story. You ever have a friend who could make a trip to the grocery store sound entertaining? That friend is a good storyteller.
A DM's Responsibilities
On the otherhand the DM has two key responsibilities: rules arbitration, and helping make the game fun. If you want to be technical, they have a third responsibility of running the NPCs be they opposition or ally, but that is tangential to this discussion.
Note though that telling a good story is not part of this. You can buy the story in the form of pre-written adventures. You can have someone else write the adventure for you. You can deliver the adventure in a very basic, hands off, almost boring bullet list of objectives sort of way. Your storytelling can absolutely suck and your game can still be fun. And on the other hand your storytelling can be amazing and your game can suck.
A lot of players don't know, acknowledge, or like this but storytelling is a shared responsibility across the table. Yes, the DM/GM/Storyteller has the bulk of the weight on their shoulders since they have the world and all the NPCs, but the Players have their part to play. Critical Role makes for such an engaging story while the game is being played because all seven people at that table are professional storytellers, and they are there to tell a story.
So if the DM is to make the game fun, and a storyteller is to tell a story, how does this work with streaming? Well, first remember that when you watch someone stream a game of D&D it is much like watching someone stream any game. You are there to watch people play a game, but you are not a participant in that game. The audience for the DM as a storyteller is not the viewers (at least not primarily) but the other people at the table.
This is true for you too. You can't please everyone. But you can please the six people around your table. Don't worry about being Matt Mercer, Matt Coleville, or whatever other GM you see on stream. Just worry about making your game fun for you and your players. That's all you need!