The US system for crochet hook and knitting needles is, not surprisingly, related. Here is a table with the metric hook sizes and their respective crochet hook and knitting needle US names. The table shows an obvious correlation between the crochet hook and knitting needle size names. Since the naming convention of hooks and needles were not standardized, there was difficulties with labeling between different manufactures. The Craft Yarn Counsel compiled the standardized nami

In some cases the pattern writer will include a crochet diagram. In these diagrams there are symbols to represent each stitch. There are even symbols for more complex stitches and stitch combinations, such as 5 dc popcorn. The pattern writer should show and define the symbols they use in their diagrams, especially if they are unique stitches. This infographic shows common symbols that are used:

Unfortunately, there is not a TRUE standard of crochet terminology, not even among English-speakers. There are the US terms and the UK terms (which is also used in Canada). Here is a quick table showing the differences in terminology and abbreviations. As a general rule of thumb: The UK and Canadian terms are based the number of loops and yarn overs there are at the end of the stitch BEFORE starting to pull though the stitches on the hook. AKA how many yarn overs there are in