Here in Perú , we call those rocks:
- Shale = Lutita.
- Siltstone = Limonita.
But as far as I know we don't use the terms claystone and mudstone in Spanish terms.
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Clastic sedimentary rocks are classified by size of the sediment particles making up the rock. Particle size descriptions like sand, silt, and clay have specific meaning in geology and engineering. (see chart below).
Shales, mudstones and claystones are rock types that are very similar to each other.
The difference between mudstone and shale is that mudstones break into blocky pieces whereas shales break into thin chips with roughly parallel tops and bottoms.
The terms shale and claystone are sometimes used interchangeably.
References: Mudstones and shales Fun rock charts on pinterest
They are all term related to the grain size, as you can read in Gary Kindel's answer.