The Collision Avoidance Regulations have been years (decades?) in the making and were the object of thorough negotiations between nations. You may rest assured that when different terminology is used, different applications are the result. That is why, if you are to continue studying these rules, you ought to get yourself a reliable reference book on their interpretation and application. The classic book is "Guide to the Collision Avoidance Rules", by Messrs. Cockroft and Lameijer. I believe the current Ed. is the 6th Ed. It is readily available on the internet and at any good nautical bookstore.
This said, on to your question: Yes, there is a difference. Think about what constitutes the classic impediment to one's passage: being the give-way vessel.
Since fishing vessels are not supposed to engage in fishing in the traffic lanes, when they elect to do so, they completely "forfeit" (for lack of a better word) any right of way they may otherwise have to any ship transiting inside the scheme. In other words, while engaged in fishing inside a TSS lane, a fishing vessel is always the give-way vessel.
However, sailing vessels and vessels less than 20m, while they should as much as possible remain in the local transit area between the coast and the TSS, may legitimately find themselves in the lanes, usually at a choke point or when crossing it. As they do so, they may very well end up being the stand-on vessel. If so, they have the right of way, unless the ship in the lane that has to give-way would be put in a dangerous situation by any action it would need to take. An example would be a sailing yawl crossing the English Channel at the Pas-de-Calais at the height of daily transits of the Channel TSS. You may have twenty to thirty ships in each direction in the lanes, all within one or two NM of each others. In such case, the yawl with the right of way would have to cede it to a transiting loaded supertanker that obviously could not safely turn, slow down, speed up or even stop in order to give-way without causing a serial collision.