You need an UK entry clearance before you leave Denmark or your carrier will refuse to board you. It does not matter that you have a Danish work permit, it is entirely governed by what type of passport you hold.
For your question about the difference between 'visa' and 'entry clearance'. An 'entry clearance' is what they will put in your passport if your application is successful. Americans, Canadians, etc who apply at the border get an 'entry certificate', or 'leave to enter'.
For your question about getting a long-term general visitor visa, if you are successful they will give you one valid for 6 months. If you build up about 5 or 6 of those AND you show them a viable need for visiting the UK over a long period of time, they will consider a longer term. A long-term visitor for ordinary tourism will not work.
Adding: take note that if you apply for a long-term visitor visa, they will keep the extra money you paid and issue you the standard 6 month visa anyway.