What journey is Frodo referring to when he talks about the treasure hunt, no-and-back again journey? How is this journey different in nature than the previous journey?

Frodo is talking about his journey to destroy the ring. 

Bilbo’s nephew Frodo had a similar experience to that of Bilbo in The Lord of the Rings. Frodo also lived a life of relative ease, until one day Gandalf also sent him on an adventure. But his quest was different. As Frodo  explained to a few of his hobbit friends who wanted to take the journey with him, “this is no treasure-hunt, no there-and-back journey. I am flying from deadly peril into deadly peril.”  Where Bilbo’s adventure ultimately led to a deeper understanding and enjoyment of the life he had before taken for granted, Frodo’s travels led to a very different place.  Where Bilbo learns courage, leadership skills, and develops as a character, Frodo learns both hope and sacrifice. These two complimentary stories have led countless readers into wonder and delight, while at the same time often helping them see their own experiences in a different light.  Like Bilbo, many people find themselves facing things did not expect. Like Frodo, many people carry burdens that threaten to destroy them, the people around them, and everything they hold dear.  Many readers have found comfort and encouragement in the stories of Bilbo and Frodo.