Welcome to the Q&A Forum

'training' is definitely considered to be a synonym of 'course' (search for "~training") - just a matter of to what degree. Run some queries in google and see how different they are. If you get the same results, they are exact synonyms. If the listings change, see how many of the same domains/pages are the same. That should give you a good idea whether they are considered close synonyms or not.