I tend to think of the difference between the two as a matter of granularity - user experience mapping is the mapping of the experience that users go through when using your product/s or service (it's about the big picture).
The user story map are the set of functions/features/tasks for that product (it's about the smaller picture).
For example, when I'm doing discovery research, I'll be mapping out the experience of the user (e.g. having a baby). Within that experience, there will be a number of products that the user will use (e.g. applying for paid parental leave). Once we decide which problem area we're tackling, we start narrowing down onto that area, and develop a user story map for that product based on the needs of the users that we had researched.
With your second question about the experience/journey map, what you map really depends upon what you're trying to achieve. We shouldn't do a journey map for the sake of doing one. But if the intent is to illustrate what the current experience is like, showing all the touch points, relevant business processes, IT systems etc, then do a current state map. This is particularly useful to have an at-a-glance illustration of the whole experience as it shows potential areas of improvements, and areas that are working well (we don't want to break those!).
It's also worth calling out that it's worth mapping not just the users' perspectives, but the service delivery experience too.
If you're doing a bit of a what-if design session, then mapping out an ideal state would be useful. But either way, everything should be grounded on good research, otherwise the maps fall into 'lovely to look at but not sure what to do with it' area. The future state experience maps should be addressing issues identified in the current state maps.
Hope this helps