An abaya is a common term many British Muslims use to denote a particular form of covering. Typically, it is worn by women in the Arabian Gulf from where it originates, and is synonymous with a robe or long dress. Men in the Arabian Gulf also wear an abaya (also a robe). It is not an Islamic garment in as much as there is no such thing as “Islamic clothing” – all clothing is cultural and either meet shar’i requirements or do not.
An abayah is usually thought of as the Quranic reference to a jilbab. Strictly speaking they’re separate things. In the shari’ah, jilbab has become a conceptual form of covering (in the Prophet’s era they associated it with something specific, but certainly not an abaya), so it can include an abayah but also many other forms of covering as well. So they are not the same thing.
Now my point isn’t to discourage people from wearing the abayah, please do as you wish and whatever makes you happy. I’m simply addressing a point on God’s Law that people tend to misunderstand due to conflating two separate things, and then haphazardly impose Arabian Gulf culture on the rest of the world as if it’s a moral virtue. It really isn’t. God the Most High neither wanted nor ordained that the world dress like Arabians, nor is it “the better thing to do” or “mustahab” – and any such assertion is silly both from a scriptural perspective and common sense. That’s not to mention that the abaya can also be worn in a way that contravenes shar’i codes on appropriate covering, such as figure-hugging manifestations, and on many occasions it is.
God’s Law outlines the amount both men and women are expected to cover and its nature, and He left it with humans and their diverse cultures to decide what fashionable form that would take. If one has an inclination to a particular cultural aesthetic then that’s fine, but there is absolutely no moral virtue in one cultural method over another (unless there are secondary factors to consider).