I think that you are describing controlled scrappy. However, there are other scrappys as well.
I've been trying to use up a lot of my scraps this year.
I've done what you say--by just sewing squares together. However, because I had so many squares, it was easy to separate them into blues, yellows, purples, etc. so I made, for example, blue and yellow squares (alternating squares), browns and greens, etc.
But here are some of the tops I've been working on this year.
This one has parts of an old red/white quilt I bought but was too holey to use as a quilt. I cut up the good parts and incorporated them here (at least some of them).
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This one has the scrappy strips around scrappy off white pieces. But it is definitely controlled. I chose only colors that coordinated with the wider strips in the middle.
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Totally random. I sewed strips together basically as I pulled them out of the bag of 1.5 strips.
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