Skincare labels use a lot of words that sound regulated and are not. If your skin is reactive, learning to read the ingredient list is more useful than learning to read the front of the box.
These two get used interchangeably and they mean different things.
Fragrance-free should mean no fragrance materials have been added to make the product smell a particular way. On an EU or UK label, added fragrance appears as Parfum or Aroma, sometimes followed by individual allergens that must be declared, such as Limonene, Linalool, Citronellol or Geraniol.
Unscented means the finished product does not smell of much. That can be achieved by adding a masking fragrance to cover the raw smell of the base. So an unscented product can contain fragrance, and a fragrance-free product can have a faint smell of its own ingredients. If you react to fragrance, the word you want is fragrance-free, and then you verify it on the back.
Essential oils are fragrance. A product can be marketed as free from synthetic fragrance while containing lavender oil, bergamot or rose, and those are among the more common sources of contact reactions. "Naturally derived scent" tells you about origin, not about tolerance. Look for oil names in the INCI list and treat them as fragrance for decision-making purposes.
Vegan means no animal-derived ingredients. In practice, that rules out things like beeswax, lanolin, carmine, some forms of collagen, and honey derivatives. It is a meaningful ethical claim.
It is not a safety, gentleness or efficacy claim, and it says nothing about animal testing, which is a separate matter with separate certification. A vegan serum can be loaded with fragrance and a non-vegan one can be perfectly bland. If you are shopping for tolerance, vegan is not the filter you want. Use it for the reason it exists.
Nothing, legally. "Clean" is a marketing position, not a standard. Different brands define it against different lists of excluded ingredients, and those lists are chosen by the brand. Some exclusions are reasonable, some are marketing against ingredients with long safety records. Treat the word as a signal of what a brand wants to be known for, then go check the list yourself.
Ingredients are listed in descending order of concentration down to 1 percent, after which they can be in any order. That gives you a few quick reads:
A plain guide to what the skin barrier is, what damages it, and how a short, single-ingredient serum routine can support it without a twelve-step shelf.
How beta-glucan and hyaluronic acid differ as humectants, which situations tend to suit each, and why the answer often depends on your climate and your moisturiser.
Why serum-strength actives are moving from face to body, what a body serum can reasonably do, and when a good body lotion is the better buy.
None of this tells you whether a product will suit you. It tells you what you are actually buying, so that when something works or does not, you can trace it to a cause and carry that knowledge to the next purchase. That is the whole benefit of short, single-active formulas: they make the list short enough to read, and short enough to learn from.