The easiest differentiator is whether or not it's an item itself. For example, 10x40 tent is not an item. It's just a collection of items (of poles and ropes and such).
Whereas a chiavari chair itself IS an item, and it just has accessories like a chair pad, a chair cover, etc.
Another difference is in the pricing:
Packages can be priced as a whole (daily, flat fee, etc) or by the items it contains — meaning the price of the package is the sum of it parts. Read more about package pricing.
Accessories are great for making contract building faster by pre-defining related or up-sell items. For example, I charge my client $10 for a chair which can include:
Chair pad (for free, optional)
Chair sash ($5, also optional)
Packages with accessories will operate the same way. For example,
Tent sidewalls (for free, optional)
Tent Bistro lighting ($$, also optional)
The accessory settings help you define those relations in advance!