What grid system is used here? modular or column?

I did some looking at the example design from Pinterest and I’m not convinced it was composed using a grid. There are some inconsistencies with how the larger and smaller letters are spaced/positioned.

Adobe Illustrator provides multiple choices with creating and using grids in layouts. You can work with a standard baseline grid. Or you can create a grid using Illustrator’s grid tool. It’s also possible to create non-square designs that can be turned into guides for attaching type and other objects. Traditionally, real grid-based design does rely on some kind of square grid.

Not every design uses a grid at all.