There is a lot of difference between a root and a leaf. They both have different roles in keeping the plant alive. The leaf absorbs nutrients from sun and performs photosynthesis, while the roots draw nutrients and water from the soil.
Now if you're asking about differences in the uses of parts of plants, the answer is still yes. Although it may vary from plant to plant. You'll find that in medicinal and more traditional forms of herbalism, specific parts are used for specific issues, ailments, or other purposes.
It really depends on the plant you plan to use. The best way that I've found to keep track of that stuff is to dedicate a spiral notebook to herbalism, then do the following:
Title a section with the plant you plan to use
Do 3 google searches and read multiple sources:
-Magical properties of (plant name)
-Poisonous properties of (plant name)
-Medicinal properties of (plant name)
Then, if the plant is poisonous, you can file your collected data sheet in a poisonous plant folder, or copy it into a poisonous herb book for future reference (if you forget the info later), and do the same if it is a non-toxic plant...if its a medicinal plant with, say, toxic roots, you could file it into the non-toxic but have a note about the toxic parts at the top of the page.
As a side note, always make sure you're researching the exact plant you want to use. Some plants, like Moonflowers, have many plants commonly called under that name, but true Moonflowers are the Datura plants, both vine and bush. Also, even though it is called for in many "flying" potions, Moonflower is highly toxic and shouldn't be used, because it can cause a violent death even in small doses and the "flying" effect it produces is really just your body's reaction to being mildly poisoned :)
Ah, I see what you mean....I'd say they would probably mean the leafy herb part in most plants, unless it specifically says the root...of course, there are herbs where it is usually only the root used, like ginger. For ivy, I would says it's the leaves and the stem :)