The C&T goblin is taken from George MacDonald's The Princess and the Goblin. In Tolkien, "goblin" is the same as "orc". The use in The Hobbit is a difference in tone compared to LOTR (that, and The Hobbit was originally unconnected with JRRT's main mythology except for borrowing some names). Orcs do come in a lot of different varieties, as is clearly seen the LOTR (the novel, if not the movies). In The Hobbit, the name "Orcrist" is translated as "Goblin-Cleaver", so while there might still be seen to be subtle shades of difference between "orc" and "goblin", they were essentially synonyms. The use of "goblins, hobgoblins, and orcs" no more shows them to be distinct races than a similar verbal flourish of "bandits, brigands, and highwaymen" indicates a fundamental distinction of three professions.
So, if you want a Middle-Earth "goblin", that's an orc (perhaps specifically one of the non-improved pre-Uruk-hai types, which would be a "lesser orc" in RM-terms). The C&T goblin is unrelated and not a Middle-Earth creature.