"I would like to go to the ocean again."
Translation:Ich möchte nochmals zum Meer gehen.
Well, if you're at the end of your vacation, you could say, "Ich möchte noch einmal zum Meer gehen (before we leave)".
It's all rather strange, on the whole: "nochmals" is very formal. I'll assume this is about "travelling to a place by the sea", so you would say "ans Meer fahren", not "gehen".
And funnily we just had the "noch einmal" vs. "wieder" discussion thread: https://www.duolingo.com/comment/25462695 - nochmals = noch mal = noch einmal = once more, wieder = again.
So if you use "nochmals", you're saying, "I want do this one more time, in repetition, reiterating". Usually you only use it in formal contexts like, "Ich möchte nochmals betonen, dass..." "I want to stress once more that [it is highly important that you meet the deadline / these are things we cannot influence, because the demands of laws must be met]".
All in all, assuming that it's about holiday planning, I'd say, "Ich möchte wieder ans Meer fahren" (like last year). If you want to say "one more time": "Ich möchte noch einmal ans Meer fahren."
(Actually you can even leave out the "fahren" altogether: "Ich möchte wieder ans Meer.")
The main difference is that you can say "Ich möchte (gern(e)) ein Bier", but not "Ich würde gern(e) ein Bier" (you'd have to add a full verb, like "Ich würde gern(e) ein Bier trinken/bestellen").
Apart from that, I'd say both are very much interchangeable. As for connotations:
"Ich würde gern(e) einmal nach Australien reisen" ("I would like to travel to Australia one day") sounds a bit better, because it could be understood as a conditional sentence as well ("...if it wasn't way too expensive for me to ever be able to afford it"), so it sounds more like you're dreaming of doing it, and possibly like there's something hindering you.
"Ich möchte (gern(e)) nach Australien reisen" sounds more like you're at a travel agency and actually want to book the trip. "Ich würde gern(e)..." would sound humbler here, so you'd prefer it for requests that might not be successful ("Ich würde gern(e) ein Foto von Ihnen machen" / "I would like to take a picture of you"), as opposed to ordering a drink or buying a ticket.
Basically, "sea = das Meer" and "ocean = der Ozean", but since I think "ocean" is more widely used than "Ozean", "ocean" would sometimes be more naturally translated with "Meer".
"der Ozean", which would mean e.g. the Atlantic or Pacific Ocean, isn't usually referred to as the thing you swim in when you're at the beach (much like you described it in your other comment: "Ozean ist zu weit"). I wouldn't even call it "im Ozean schwimmen" if I jumped off a cruise ship in the middle of the Mediterranean Sea.
If I jumped off in the middle of the Atlantic Ocean, I'd probably still call it "im Meer schwimmen" - or "aufs Meer hinaussehen" ("to look out to sea") while standing by the railing -; but if I want to stress the vastness of it, I can certainly call it "Ozean". And for crossing the Atlantic on a ship, I'd much prefer "den Ozean überqueren" (instead of "das Meer").
When I first went on holiday on the Canary Islands, after several holidays in the Mediterranean, it was a mentionable thing that the sea you swam in was the actual Atlantic Ocean and the next big chunk of land was faraway America. I still wouldn't have used the word "Ozean", because it would have felt unnatural or overly poetic to me; we called it "der Atlantik", if we wanted to specifically refer to "the big wide ocean between here and America that often brings bigger waves to the beach". Else we'd just call it "das Meer" as usual.
That would either be "I like/enjoy going to the sea/ocean once more"; "ich gehe gern..." in this case would describe a hobby, something you regularly enjoy doing, and thus doesn't work with "nochmals / again".
...or you could use this if you're working at a hotel and have been looking for an object a guest has lost on the beach, and they say you probably haven't looked enough, and you reply, "I'll gladly go to the sea again and check for you."
So neither translates as "I would like to go to the ocean again".
Ich habe die erwähnte Antwort gefunden: "Das Meer is used as a general term for the water surrounding all continents, while Ozean is usually a specific ocean, like the pacific, atlantic, .... But that's not a strict rule, also Ozean could be accepted here, Meer is just common as a habitat. On the other hand, also Meer can be used in specific names, like Kaspisches Meer, Nordmeer, ...." Es ging um den Satz: "Squirrels do not live in the ocean." -> "Eichhörnchen leben nicht im Meer."
It would be really helpful if there was an actual lesson that went with this bubble.
English sentence: "I would like to go to the ocean again." This indicates that the speaker has previously been to the ocean and would like to return to it.
German translation: "Ich möchte nochmals zum Meer gehen." "nochmals" is (apparently) modifying "möchte," not "gehen," meaning something more like "I would again like to go to the ocean," which says nothing about whether the speaker has ever been to the ocean, only that they have a recurrent desire to go there. Shouldn't it be "Ich möchte zum Meer nochmals gehen?"
The word order: "wieder zum Meer gehen" - "wieder" refers to the whole action of "zum Meer gehen" and thus precedes it.
"Ich möchte wieder die Katze streicheln" = I've just arrived at the animal shelter and tell them I'm here to pet the cat again (not to take the dog for a walk).
"Ich möchte die Katze wieder streicheln" = I'm tired of brushing the cat, I would like to go back to petting it.
"Ich möchte wieder mein Auto verkaufen" = I've sold you two cars before, and once again I'm here to sell you my (another) car.
"Ich möchte mein Auto wieder verkaufen" = I bought this car last year and now I want to sell it again.