You can see how that could be confusing given all of the different Outlook-related products and services out there today, but that confusion isn’t just a recent thing.
Consider the now-defunct Outlook Express, which was an email client that came packaged with Internet Explorer starting in 1996.
Next to Gmail, Hotmail was one of the world’s most recognizable email services.
So as of right now, is the official name of Microsoft’s email service, which was formerly known as Hotmail and Windows Live Hotmail. Whenever you said “Hotmail”, people always knew what you were talking about.
Remember how Microsoft wanted to rebrand Hotmail as Windows Live Mail? Hotmail became Windows Live Hotmail while Windows Mail became Windows Live Mail.
On Windows 10, none of the above-mentioned programs are relevant except for Outlook (which can also be called Office Outlook if you want to differentiate it from all the other Outlook-related products out there).
At the time, Office 365 was geared towards business and corporate users, but over time it was expanded to include regular consumers as well.
In a lot of ways, Office 365 is what Windows Live should’ve been.