Crochet goes back a long time in history, the simple craft of taking a ball of yarn and a hook and turning it into one of so many things was later turned into knitting by the french by using two needles instead of a hook to achieve similar but yet different results.

Much like some of the ways language has changed between the UK and America, so have terms for crochet.

If you're learning online its quite likely the terms will be american, if you're purchasing patterns or books, its not uncommon for it not to state wether its using US or UK terminology.

US term                                UK term
Slip                                       single crochet
single crochet                        double crochet
half double crochet                extended double crochet
double crochet                      trebble crochet
trebble crochet                      double treble crochet

Often the easiest way to find out if you're reading an american or UK pattern/book is to go either by hooksize - which americans will usually have 14 - 0 then A-Z  where as UK needles are often just referred to in modern books by their size in mm. Or check