Summary
Video game remakes are the bread-and-butter of the current video game industry. If a game exists, you may bet it exists in at least three other forms, too. This is great if you like playing the same game over and over, not so much if you like to play brand-new things. Though some remakes decide that, well, it should be more than a remake.
Some video game remakes, reboots, reimaginings want to be more than the original game with a new lick of paint. It is a new game, and it should act like it. Some of these remakes like to take the story further in a very literal sense, taking that original plot and expanding it beyond the realm of the original. Not just deeper, but further.

After Hitman: Absolution took the series in a decidedlymore action-based, linear direction, Hitman 2016 was intended as a return to form. Not strictly a remake, but a way of bringing back that original style of gameplay with a fresh slate. Except despite how disconnected it seemed, this game just so happened to be a direct continuation of Absolution.
Reading into some of the dossiers on your targets will have direct references to previous targets, and brief allusions will be dropped by your trusty handler. If the 2016 game wasn’t enough to sell you on it, then the sequels will. The literal family members of previous targets appear, and in Hitman 3, the story is a direct contiuation of Agent 47’s personal story.

The strict continuity of Metroid is a bit complex. While the side-scrolling entries were the original games, Metroid Prime is the more prevalent game. Except it’s story is off to the side, squeezed between the original Metroid, and Metroid 2. But then Metroid itself has an actual remake in Zero Mission, which expands upon the story of the original game.
This has enough to fit the criteria of being a sequel, but Super Metroid takes it further. While not officially a remake, it retraces the steps of the original game almost 1:1. You are on the same planet, going through the same regions, fighting the same enemies, and even have the same final boss. Super Metroid is conversely a sequel that is also a soft-hand remake.

When you want to talk about continuity, then Nier is a real winner. Nier itself is a sequel series to Drakengard, and Replicant continues into Automata. Except with the Replicant remaster/remake, it flows into Automata in more ways than one. You see, Nier has quite a bit of extended media. It is mostly supplementary, but fills in the gaps between games.
In the original Nier Replicant, ending D continued into Automata, though this still left some blank spots, which were filled in with a novel. This version of Replicant howeveradds ending Eon top of this right at the very end. This acts as a continuation of Kainé’s journey, and is also an adaptation of The Final World novel, directly linking the game with Automata.

5Layers Of Fear
Before Bloober had its first actually beloved game in the Silent Hill 2 remake, the studio achieved prominence with Layers of Fear. Heavily inspired by the Picture of Dorian Gray, Layers of Fear followed the demented mind of a painter and his many family issues. The sequel was completely disconnected, making the series an anthology of stories instead.
Ad then came Layers of Fear, a remake with the name of the original game that compiled both games together. For the most part, they still acted as two separate games, though now at a similar graphical level. Except each story got one additional story segment, furthing expanding the plot of both.

It is rare, in more recent years especially, to get very many Zelda game spin-offs that are not remakes or remasters. Games take longer to make now. Even the remakes we do get are mostly 1:1, though with a new art direction. A Link Between Worlds straddled this line in such a unique way though.
Being a remake, sequel, and independent game all in one, A Link Between Worlds took the world of A Link To The Past and reinterpreted it to present a new story featuring Lorule. Ah, but Yuga is trying to freeGanon after his original banishmentin A Link To The Past. And Hilda seems to allude that Lorule used to be the Dark Place, but that it grew into a land of its own after Ganon was banished.

If all that wasn’t enough, the game is literally called A Link To The Past 2 in Japan.
In the age of video game remakes and reboots, many of them play it safe, choosing to recreate the original with few changes beyond graphics. Others attempt to style this new game after more recent industry trends rather than those that made the original work. This is the camp which Thief (2014) falls into. And it is messy.

There are a lot of interesting ideas at play here, but the whole vibe is just off. For all intents and purposes, it would seem like a complete reimagining. There are illusions to older elements, such as the Pagans and automatons, and even some of the more mystical elements are alluded to. It’s light stuff, but enough to indicate the game takes place past the originals.
The Thief reboot was originally titled as Thief 4, so that’s another link to its place as a sequel.

The Silent Hill 2 remake is an impossible game, managing to bypass many of the failings of Bloober’s own games in terms of writing and horror, while still presenting a new rendition of the game that strikes its own vision while still playing close to the original. While never strictly confirmed, it seems it may be a successor in more ways than one.
A long-standing theory is that the Silent Hill 2 remake is set in a time loop. Even the original game alludes to this in the Maria ending, but the remake goes a step further. Secret messages in hidden photos, glimpses into the past at set locations, new content in New Game Plus, and the new endings themselves, too.

Perhaps the most high-profile video game remake there has ever been, Final Fantasy 7 Remake achieves something that should have been impossible. It is exactly what it was described as - an expanded version of the Midgar section of the original, though approximately following the same story. It was that, until it wasn’t.
There are breadcrumbs throughout the game, but the ending makes it quite clear - this game is more than just a remake of the original FF7, but a parallel universe. The events of the original still exist, and this is another world wherein things have deviated slightly. Hell, you literally defy fate at the end of the game to allow Rebirth to deviate even further from the story.
