Hello!
If I'm understanding correctly the question, you are expecting rectangles when viewing the grids of spatially projected map data. I'm not sure on your background understanding of spatial references, coordinate systems, and the nature of mapping 3d objects into a 2d plane but I think that is where you'll find a more complete answer to your question.
In short, while grids on maps and diagrams may look like rectangles or parallelograms, there are very few instances where a line drawn straight on a map would appear straight on Earth or visa versa. Flat maps are representations of 3d data (in Earth's case, a geoid) and thus always invite some type of distortion in how they are represented. This will depend on spatial reference used (which depends on a particular geoid model of Earth), projected coordinate system, and scale of viewing.
So while grid lines on different maps may appear to have a rectangular shape or other shape, they tend to be representations of what a straight line would be on the surface of the geoid model used to represent Earth. On the surface of the Earth, those lines would actually appear to meet at a 90-degree angle as you suspected. It won't always appear that way in a map however depending on spatial reference, projection, and scale.
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The following resource may help shed some additional light: Spatial references | Documentation | ArcGIS Developer
