Everyone knows the history of the game since launch so lets bypass the comparison with how it launched and go straight to how it is now. Also let's bypass what Fallout is and assume that you already know.
Is it Fallout?
Yes, like the other games its catered to a certain area which is unique in its own way, Fallout 76 is a modern version of the game.
Are you avoiding it because it's online?
Stop worrying and give it a go, Appalachia is ready now and waiting for you. I was cautious on this one and held off several times, but once you give it a go, you will see it isn't a factor and actually enhances the experience for this game (not saying there isn't a place for single player Fallout).
Can you play solo?
Yes you can. You don't need to play with others, have a crew, play it a specific way at all. The online component is there to enhance the experience, but you don't need to worry about it at all if you don't want to. Community events can be joined and left at will without needing to know or join anyone.
Do you need to pay a subscription?
Its up to you, the game is completely playable without it. I have played with on one on and off and its handy but definitely not essential. Certainly up front play it without Fallout 1st and make your decision while playing if you need it or not.
Do I need to buy things?
No. You really don't, there are a lot of free elements around that will keep you active, any purchases are there to enhance the base game for those that want them. There is enough to do and see without needing to purchase.
What is the community like?
Its one of the (if not THE) best online communities out there for online games, don't be afraid to start out and see big numbers on player levels, most are more than generous helping out new players and making sure you get a positive experience from the game.
Is it like the TV show?
It's a different part of the overall story, but factions are the same and there are a lot of familiar elements. There are also updates coming to cross over a bit more if that is what you are after.
Is there replayability?
Yes, you can play as long as you feel like you have interest in it. Once the story has finished there is still a lot that can be done with events, challenges and general exploring of the map. Every season brings new challenges and things to do with it.
What are seasons?
Seasons are regular releases of Fallout 76 that introduce events, sometimes areas, updates, tweaks, new gear. This is all layered onto the base game, so the core story isn't impacted by seasons.
Why shouldn't I play?
First and foremost, if you don't like Fallout is a good first start, its post apocalyptic and very styalised to a certain feel. It also isn't just a FPS, there are all sorts of elements in this game that expand on just being a shooter.
If you are a Fallout purist, there are things and items available to build at times that might make you feel a bit like its not cannon or is not really Fallout. These aren't major and are mostly aesthetic items people build at camps, but its a consideration all the same.
You are looking for a quick play, Fallout games are not a quick finish and take time. Most players have several hundreds of hours in the game so if you are looking for a quick turnover this isn't the game for you.
Why should I listen to you?
If you are still reading down here, just give it a go.