If Golos, Tireless Pilgrim's activated ability were to hit a adventure card are you able to cast the adventure side of the creature or only the creature for free? Rules on Golos say you may not use alternative costs, and rules on adventure state an adventure is alternative characteristic? Is the same thing worded differently?
You can do both.
715.3. As a player casts an adventurer card, the player chooses whether they cast the card normally or as an Adventure.
Playing a spell is the same as casting it. You're right that the adventure mechanic does mention alternative characteristics, but this is different from alternative costs.
118.9. Some spells have alternative costs. An alternative cost is a cost listed in a spell’s text, or applied to it from another effect, that its controller may pay rather than paying the spell’s mana cost. Alternative costs are usually phrased, “You may [action] rather than pay [this object’s] mana cost,” or “You may cast [this object] without paying its mana cost.” Note that some alternative costs are listed in keywords; see rule 702.
Yes, you can cast either part for free.
When you cast the spell, first you choose if you are casting the creature or the adventure. After you make that choice; you apply alternative costs; which includes “without paying their mana cost”. Nothing in Golos’s ability is restricted to applying only to creature spells or sorcery/instants; so it would apply to either.