Yeah, maybe I'm using the wrong word.
What I want is to have the player follow the story as I want, but I'd like for them to have some other things to do like exploring and finding secrets I guess?
Okay, yeah, so depending on the amount of exploring and non-main-quest action the player can partake in, and (this is really important) how much control the player has over
when they can partake in these things, the game will be considered either mostly linear or mostly non-linear.
On the mostly linear side of things (
Star Ocean,
Final Fantasy 6,
Grandia) you as a designer are not unlocking areas or additional content until the player plays through the main story to a point that those areas are now relevant. Most players will find them in approximately the same order. To make it feel like "less of a straight corridor", you can make the areas large and heavily explorable (in the sense of players can wander off the main path but don't need to), and add things like sidequests or even a few main plot objectives that require traveling back to towns you've already visited. These games and their activities are often driven by plot.
On the mostly non-linear side of things where things are still structured around a linear main story (
Persona 3,
Recettear, story-oriented
Civilization mods), you are giving the player the freedom to do nearly anything they want with their time, participating in activities that are somewhat divorced from the main story objective. Along the way, assuming the player is finding success rather than game overs, you tell the story in a linear fashion, unlocking a few extra elements that would only make sense once a certain part of the story has been reached. The main thrust here is that at least most of the time, the player can choose between entirely different activities that all feel like a "correct" way to play the game, which is a lot different than simply having a sidequest or minigame along the way as a diversion. You want a lot of different areas to be open to exploration and activity at any given time and you don't want the player to ever feel like they're "wasting" time participating in them. These games and their activities are often driven by time or exploration.
In the middle (
Dark Cloud,
Jade Cocoon,
Rogue Galaxy) you unlocking locations in a fixed order and telling the story as the player completes them, but introducing large numbers of optional objectives, deep side activities, and a big, replayable (often semi-randomized) world in which to do them. An objective might be "construct a temple to move on with the plot" but instead of your characters saying "let's get the one necessary ingredient by killing the boss in the nearby dungeon", you might be tasked with finding easily-gatherable materials throughout the world and finding one of several people who can help build the temple. These games and their activities are often driven by objectives and gameplay.
It all comes down to what kind of experience you want for the player. Be sure you can verbalize that experience, because if it's something that's nebulous, or only in your head, you are not going to be able to focus on making the best form of that experience possible. In any case, I hope this helps you figure out what kind of linearity and freedom you want to allow in your game!
