The difference is ore specific. Crushing is employed as first step in size reduction and the may consists of 2-3 substeps. Crushing breaks the large particles into multiple pieces and the aim is to facilitate easy transportation and storage. Generally +20 mm is acceptable for crushing.
Grinding is a more controlled process and the size that can be achieved is in micron level.
Crushing is classified into to primary and secondary processes in which the size is reduced from large lumps, can reach 1m, to 2mm like the jaw crusher. The grinding is used to obtain finer fractions than 2mm