In the formalism of both this article and https://news.ycombinator.com/item?id=37517118, "base units" are specially designated physical quantities, while "dimensions" describe how physical quantities scale under changes to the scale of measurement.
Customarily, capital letters like M, T, L, etc., refer to dimensions, and you would something like [1 kg] = M to say that 1 kg is a quantity that scales like a mass. A PLT analogy analogy would be to compare physical quantities to values and dimensions to types.
In practice we can refer to dimensions by base units, but it has some mathematical benefits to view them as distinct. Hope that clarifies things!
