There's no expectation that it might. Muro is based on "tabby, calico," i.e., on the coloring of a cat's fur. A "tomcat" is kocúr in Slovak.
Muci was the default name of any cat we owned ... probably coming from the Slovak/Moravian side of the family
Both
muci and
cica are pretty common words for "cat, kitty, pussycat" in Hungarian.
Macska-Matska) just means cat
Pronounced [matshka]. Hungarian borrowed it from the
Slavic languages around it, all of which have
mačka like Slovak. It may be related to
maco/macko [matso/matsko] based on "fleshy, chubby" and used as a
nickname for "bear, teddy bear" in Slovak, borrowed as
mackó in Hungarian.
But the word
kočka [kotshka] became common for "cat" in Czech a long time ago, perhaps under the influence of the German
Katze, and variations on
kot are used for "cat" in the rest of the Slavic languages, with the same origin as the Slovak
kocúr, "tom cat": the versions in
k- are from the Latin
catus that also gave
cat in English and similar words in the other Germanic languages.
The fact that the word for an animal we think of as so commonplace today actually needed to be borrowed "from the south" shows that cats didn't used to be in Europe in the distant past. They spread from the south and their name traveled with them.