You can find a better documentation here: D3DXMatrixOrthoOffCenterLH and D3DXMatrixOrthoLH.

TLDR: use XMMatrixOrthographicOffCenterLH if you don't need to move a camera as this is simpler and it's one less matrix multiplication to do (since you don't need a view matrix) Otherwise you will have to use XMMatrixOrthographicLH and also provide your own view matrix.

I was going to post something yesterday but I wasn't 100% sure I was correct but seen as you haven't had many responses I'll post anyway but bare in mind I might be slightly off.

Both are creating an orthogonal projection but one is more flexible than the other. XMMatrixOrthographicOffCenterLH essential also contain your 'view' position, it will move your camera to the centre of the area you define. For example, if you set the left to 0 and the right to 800 then it should (I believe..) make it such that the left is 0, the right is 800 (unsurprising) and your camera is at 400. You don't really need a 'view' transform with it. That is probably the better choice for you if you have a static 2D game/window without scrolling.

XMMatrixOrthographicLH almost does the exact same thing but it doesn't contain a 'view' (well it kinda does with the z axis). If you set width to be 800 then the left of your screen will be -400 and the right of your screen will be 400. It will make it such that your 'view' s at 0,0. That will be good if you intend to have your own view transform that you want to move around yourself such as a side scrolling platform type game.

You can see what is happening from the links that NikitaBlack provided. The bottom row can be thought of as the translation, for XMMatrixOrthographicLH the x/y values of that are set as 0 but they are not for XMMatrixOrthographicOffCenterLH . You could use XMMatrixOrthographicOffCenterLH to create the same matrix by using left=-400, right = 400.

The third column/fourth row element looks different in both zn/(zn-zf) versus -zn/(zf-zn) but actually they are exactly the same if you rearrange them algebraically. Not sure why they are arranged differently there.