Some terms have a specific meaning and others have a general understanding. You aren't always going to look it up on Google and sometimes even that might not help a whole lot. So, here is our interpretation of these terms in reference to the beauty, cosmetics and fragrance industry.
Clean: No harmful chemicals used.
Why anyone would do that anyway, right? Some chemical components can be controversial, some bring down the cost while the risk factor seems low, and some are less volatile and increase the shelf life of a product - there are just assumptions about possible reasons. We honestly believe that no company uses truly harmful chemicals in their products. There are also many regulatory bodies to ensure this as well. Most products go through a lot of testing to make sure that the guidelines are followed.
We follow IFRA guidelines for our fragrances and also try to use the best quality material v/s cheaper alternatives. Natural ingredients are used wherever possible and their complex beauty certainly appeals to us a lot. 
Green: Made from natural ingredients only.
At least that is what we think when this term is used. We don't claim to fall in that category, because -
- For some ingredients it can be too much of a burden on Nature to provide in the quantity it is demanded in. Thanks to ever-advancing technology in all fields, it is much easier to find high-quality synthetic alternatives.
- Natural essential oils are very volatile and some are more likely to cause allergic reactions compared to their synthetic alternatives.
- Source of some rare natural ingredients can be a bit on the side of unethical practices. We'd rather stay cruelty-free in all aspects of sourcing our ingredients.
- There are many synthetic molecules that do not have a natural alternative and can often provide some oomph and beautiful dimension to a fragrance structure. We do not want to miss out on that opportunity wherever suitable.
Having said that, there are some great green beauty and fragrance brands that we absolutely adore. They seem to have figured out ways to do this balancing dance really really well and we respect that very much. 
Niche: High-quality product not available from too many sources or available in limited quantity.
It is probably one of the most controversial terms.
Apart from being exclusive in availability, it can also imply that the creation process is more thoughtful, thorough and adheres to certain standards. This term can also indicate expertise or specialty in a certain field - for example, a brand that mainly indulges in creating fragrance products only and works with expert noses.
A better way to look at this, particularly in the fragrance industry, is perhaps by looking at the market it targets. Simply put - if a fragrance isn't trying to capture the attention of masses and rather wants to do its own thing in hopes of appealing to people who care about finding something unique and inspiring, you can gladly call it Niche. 