Copying all files of specific type to a specific folder using Mac's Terminal
You should be able to just run

t=${TMPDIR:-/tmp}/target
mkdir "$t"

find . -type f -name '*.STY' -exec cp {} "$t"/ \;

mv "$t"/* ./styleFiles_chekad/
rmdir "$t"


The idea behind using a temporary directory is to prevent find from also copying the files it already moved into ./styleFiles_chekad/.