Of course it's all multiplication, and all essentially the same thing. I find the grid method the least notation-focused of at least these three, and so I think more accessible to assimilation. Maybe I'm biased, I didn't learn multiplication this way but found myself naturally doing it like this in my head and then was pleasantly surprised to find it had a name. It's also amenable to estimation.
(1 + a)^2 = 1 + 2a + a^2
Thinking about approximations when a << 1, you can motivate why
(1 + a)^2 ~= 1 + 2a
In other words, keeping this grid picture in mind can be helpful to more mature mathematicians/physicists/engineers...probably more useful than the standard multiplication algorithm is.