Yes most cruise ships,cargo ships etc still burn some sort of mfo. Marine Fuel Oil. So thats plentiful around the world. Its been around since the 1900s. Lng is still relatively new technology. You could compare it to the electric vehicle industry. There's a gas station on just about every corner but electric charging stations aren't as easily found. For now. That should change in the near future. Same thing with lng. It will catch up over time as it's still relatively new technology compared to mfo. Back at the turn of the 1900s the US Navy started to change from coal to mfo. At 1 point they had 2 or 3 ships that were non coal and had to send some battleships and their escorts over seas. I forget why off hand. Long story short, the USS Arizona, which was one of the first non coal ships, got to stay behind while the rest of the fleet went over seas because mfo wasn't readily available. Flash forward 20 years or so and everyone is using mfo with coal about done. Today everything is mfo or turbine combo. If its not nuclear.
Lng is different from mfo in that in its natural state, lng is a gas. To store it, its chilled to minus 260 degrees Fahrenheit to become a liquid. Reason is that lng expands 600 times from liquid to gas so you can store more as a liquid. It has to be filtered cleaned and dehumidified 3 ways to sunday for safety before being chilled. Any impurity could be bad. Its also stored under about 5 psi, so if there was a leak, nothing would come in, only out. Theres a specific process that goes into transfer. For example beside grounding or bonding everything to guard against sparks, pipes and hoses have to be purged and chilled before pumping starts.
As far as the actual storage, the tanks are typically a sphere but can be any shape,since its low pressure and their insulated heavily to keep them cold. Since lng is colorless and odorless I would expect some type of mercaptin added also to help detect a leak, as well as sensors at specific locations also, which is something that mfo doesn't need. They can get by with level alarms and retaining walls.
As far as delivery, not much changes. The barges look similar, but the main difference is procedure. Like I said, everything gets bonded and grounded, purged and checked where mfo, hook up, push a button or 3 and look up.