Borderlands is not open-world in the same way that GTA and Skyrim area. It isn't one huge map that you can explore freely. You zone between areas. Some of the areas in Borderlands 2 were fairly large, but nothing like you'd see in an MMO.
I would describe Destiny as a mix between the two. Each area like Old Russia is actually a pretty huge area. There are a lot of "sub" zones with different level creatures and stuff to do. Some of these can be fairly large, some of them are fairly small. But combined, it takes me ~10 minutes to go from one end to the other even using the vehicles. There are no loading screens in these areas.
On the other hand, you then have to jump to orbit to go to different areas. Old Russia is the only area we have access to right now, so I don't know the names of others. But apparently there are 5 on Earth and more on the moon, mars, etc.
This clean division is complicated by the story mode though. In story mode, you will jump between missions. There are multiple missions in the same area. Each mission will land you in a different area of Old Russia with different objectives. These areas are connected to the larger Old Russia map. However, when in mission mode you enter special "Respawning Restricted" areas that are for you and your fire team only. They are sub-instances of the map where party specific special events happen. I would note that the entire area the mission is in is generally not these special areas. I frequently saw other players while trying to accomplish the story missions. Only areas where you have a specific task to complete are generally respawn restricted.
So playing through story mode, it can feel like you are playing a bunch of really small areas that require you to go to orbit and jump back down fairly frequently. In other words very non-open world. However, in exploration mode you can visit all of the areas you have unlocked through story mode in a fairly large "open" world.
It is actually pretty difficult to explain until you've played it a bit. Took me a while to figure out what other players could and couldn't see, where I would run into other players, and what places I could go into when in story mode vs exploration mode.