Is there non-linear gameplay with multiple ending?

Can the player make choices that affect the story and may result in multiple endings, or does it consist of going through linear levels while always telling exactly the same story?

I do not count such things as modifying weapons or your gear as relevant. I also am not interested if I can defeat foes in different ways or avoid them altogether.

Yes, the game is extremely linear - there is always only one path to take, and only one ending.

However, don't let this scare you off: the storyline and atmosphere are amazing, and definitely worth playing.

Also, since you mentioned it: you can mod your weapons, and in some cases choose to fight, avoid, or (sometimes) run away from enemies. There are also many different ways to fight enemies, if you choose to do so.

The Last of us wiki has a section on game-play that says:

The gameplay will be "less linear" than the Uncharted series, even though it will not be open-world. Instead "the exploration will be more important and will have enough weight in the gameplay.

Whilst the wikipedia page on the last of us describes the plot, in detail so many spoilers, to be linear.

So from the looks of things, you cannot change the way the game ends, but you can take a few different paths, (literal paths through buildings or a subway ect), to get there.