It probably doesn't - you are the one who can see the plan - we can't, and rarely are the plans accurate enough to judge exactly what the deal was all those years ago before 4x4s and pathetic drivers were invented.
However you would be able to see from the plan whether a T-section is shown, suggesting a turing space.
Unfortunately these situations just have to be challenged and see what outcome you can achieve by 'peaceable means'. You want really an agreement that you can live with. Write them a brief note on what you've agreed if you want - they way there is no danger of them achieving an extension to their existing right of way. The last thing one wants is an escalation of the problem; equally one doesn't want to be spending money on lawyers. The trouble is that 'arsy people' seem to feel they can get away with this sort of abuse of their neighbours. And to a certain extent they can - merely to maintain a modicum of peace.
A (private) right of way and a right of access are the same thing. An easement is a generic term for a right one person has over anothers' land. There are many sorts of easements - for example, a right of way, a right to water, to right to free passage of drains through another's land, a right to light. Etc.