Ah, okay. So you have having trouble with your curved mesh.
For a tile-based setup, you need to make sure the vertices of the two (non-curved) edges are in the same locations (relative to the center of the mesh) as they are on the square mesh, so that they meet at precisely the same location without any gap. You can go into edit mode (tab) and adjust the positions of the individual vertices by entering them in manually into the transform panel. Use the n key to toggle the panel on and off (scroll to the top). If your square is 100cm along x and y, then the lower right vertex is going to be at 50cm(x),-50cm(y) relative to the center.The lower right vertex on the curved mesh should have the precise same coordinates, but it is probably off by a little. Just manually enter in the correct coordinates. Check all three of the vertices on the straight edges of the curve mesh.
Also, if the mesh has any thickness to it (not just a plane, more of a box), you need to do that for both the top(z) and bottom(-z) set of vertices.
From that picture it looks like your mesh does has thickness to it, and the vertices of the right hand face are not aligned, and you have a sort of steep slant from the top to the bottom vertices. So you will need to manually set the coordinates for all 4 vertices to flatten out that right hand face and have it exactly where it needs to be.
This won’t help with precision (still need to manually enter coordinates for that) but a quick way to flatten a slanted face like that is to scale the vertices of that face on the axis perpendicular to the face. So in this case scaling all the vertices of the right face on the x axis. Scale it down to 0 and they will all be aligned.
Quick tutorial: First change the viewport shading to wireframe (selection is easiest in wireframe) and drag a box to select all the vertices on that side, and scale (s key) and then lock the axis (x key for x axis in this case, y or z depending on situation) and scale them dragging inward while holding the ctrl key (it enables snapping to even increments). There is a little readout on the bottom of the viewport that will tell you how much you are scaling by, and you want to do it until it says Scale X: 0.000. Very useful for flattening a whole group of vertices when you want.
Just keep in mind when manually inputing vertex coordinates that those coordinates are relative to the mesh’s center/origin. Those coordinates don’t change if you change the object’s scale (distinction between mesh and object). That is what apply transforms is for (ctrl+a). It updates the mesh so the vertex coordinates reflect that new size (relative to the mesh’s center). So if you doubled an object’s scale, and used ctrl+a, now the vertex is twice as far from the mesh center, and the object scale returns to 1 (instead of 2). I mention all this since it’s important to keep in mind when exporting from blender (like fbx) so that things are exported as the size you intended.