This is one of those thing that, unless I look at it, I really can't imagine how to reproduce it. But it sounds like one of two things. Either it's a "greycoat" plaster or a "knockdown". Greycoat is like a cheap plaster that was put up as an initial fill and was never meant to be the finish surface. A finish plaster was usually applied to provide a smooth surface. I have stripped wallcoverings and uncovered greycoat many times, and then had to skim to get a decent wall.
Knockdown texture is a texture that was applied either with a brush, sponge or sprayed on with a texture gun (like the kind that is used for "Popcorn" ceilings). Before the texture dries, a taping knife is drawn over the wall to knock down the high points leaving a texture very much like what you have described.