No, they are different versions; Windows 8.1 was an *update* (as opposed to an upgrade) to 8, like SP1 was an update to Windows 7, but there various versions of 8 as well - there's 8 and 8 Pro, which updated to 8.1 and 8.1 Pro.
Windows 10 is the same way. Windows 10 is like Windows 7 Home and Windows 10 Pro is like Windows 7 Professional. The free upgrade that Microsoft is offering works along these same lines - if you currently have Windows XP Home, Windows 7 Home, or Windows 8, you could upgrade to Windows 10 for free (on that machine only); likewise, if you currently have Windows XP Professional, Windows 7 Professional, or Windows 8 Pro ( 8.1Pro), you could upgrade to Windows 10 Pro for free (on that machine only).
If you have Windows 10, and you want Windows 10 Pro, you'd have to pay to upgrade.