"Get started" is a so called "get passive" in the form, but it is used as an intransitive verb. It is very frequently used in speech in the meaning of "start work" or "start to be active". (EX) Come on, boys, let's get started!
"Getting started" is a present participle or gerund of "get started". As seen in the page linked by W3, "getting started (with X)" is a phrase routi