As I realized when I first looked at London tube maps, in British English, journey basically means trip. In American English, the word is almost always used either metaphorically or to refer to a really long and momentous trip–journey though life, journey into terror, journey to the center of the earth, etc.
Are we starting to adopt the British use? Well, maybe. Megabus–a Canadian-owned company, admittedly–is big on journey. (They also ask for the expiry, rather than expiration, date on your credit card.) And an item in the June 3 Hattiesburg (Mississippi) American notes, “TripIt is one of many apps that helps you organize your journey.” (Possibly the writer was using elegant variation to try to avoid repeating trip.)
Meanwhile, perhaps British use is changing as well. I note that the new Steve Coogan film about a journey (literal and figurative) he takes with his buddy is called “The Trip.” Stay tuned.
notoneoffbritishisms.com 
That band popular in the 80s wouldn’t have done nearly so well if it were named “Trip”.
I’ve tripped over journey occasionally, but I think it will continue it’s present course in the near term.
Megabus is owned by Stagecoach – a scottish company. I suspect the took the britishisms over with them.
It’s odd.
The journey is what we in the UK take. The trip is what we are on.
In other words, the journey is how we travel to somewhere, the trip is the holiday (or vacation!) itself.
“How was your journey?” “It was fine, the train was only delayed by 15 minutes.”
“How was your trip?” “Blackpool was wonderful, it only rained four days out of the five.”
Having said that, obvious, being British, we like to use them as generally interchangeable as well. No use having only one word for something when you can have five or six or more!
A trip, in Brit Eng, is a journey made for pleasure. That’s why The Trip is so called. One doesn’t have a dialy trip to work, aor have a trip to one’s mother;s funeral. Those are journeys.
journey is formal, trip is more informal.
i.e. “I journey to work everyday” but “I took a trip to the beach last week”. One is formal and regular, the other irregular and informal.
Just ngrammed ‘trip to, journey to’. In BrE ‘trip to’ overtook ‘journey to’ in the early 1980s, possibly coinciding with the increase in overseas holidays, possibly reflecting growing AmE meaning. In AmE that happened in 1915. I find it interesting that journey is at the same level in both corpora (.0003-0004%), but trip is twice as frequent in AmE cf BrE (.001% cf .0005%). Maybe this reflects that, living in a larger country, Yanks need to travel more than Brits.
Interesting results from an ngram of “enjoy your trip, enjoy your journey’. No one in either country seems to have travelled for enjoyment much in C19. Very few Americans enjoyed a journey before 1990, finding trips much more enjoyable, but by 2000 journey is at half trip’s level. The BrE results bear out what other commenters have said: that British trips are by their nature enjoyable and journeys much less so, apart from a couple of brief spikes just before WW1 and during WW2. There was a wartime poster released in 1940 that asked: “Is your journey really necessary?”, which may be related to the spike.
The AmE usage must be why people on reality shows (on both sides of the pond) often talk about being on a ‘journey’, which sounds weird to British ears, but then ‘trip’ would sound weirder.
Calling a film “The Trip” may tease potential audiences that it will involve drugs. I cannot believe that those involved were unaware of this. No such connotations attach to “The Journey.”