How fuzzy matching is transforming interfaces
Summary: A number of innovative interface features are gradually improving our collective user experience of software.
Google, Sublime Text and Ubuntu all have something in common: fuzzy matching.
It is the grooviest thing. For example, I simply type in "fuzzy m", and magically the first search result is Fuzzy matching - Wikipedia, the free encyclopedia. Likewise, with the Sublime Text editor, I type Shift + Cmd + P and up pops the Command Palette, with the next command only a keystroke or two away. And ditto Ubuntu's Unity desktop, with the Intent Driven Interface aka Heads-Up Display — now with added advertising.
What fuzzy matching does is make it easier to search than to type or move a mouse. Now when I'm working on a web project, I rarely use the Sidebar for locating and opening files in Sublime Text. Instead I use Cmd + P to bring up Goto Anything, which is far faster.

Anything that reduces clutter and speeds up the interface is welcome, and for touchscreen-savvy websites, another example — this link needs a touchscreen — is off-canvas panes. All these incremental changes are slowly improving our collective interface experience.
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Talkback
Yes, definitely improving UI
Useful hint
Not that fuzzy...
When I hear "fuzzy matching", I think of systems which find similarly spelled (like when Google changes "aviaton pieonears" into "aviation pioneers"). Now, according to Wikipedia, your examples are also correct, as Wikipedia only really says that it finds matches which are "less than 100% perfect". Granted, finding matches for "Mozambique" when you've only typed in "Mozambi"... your search term isn't perfect, but only because you haven't finished typing it yet. It's *much* easier to search a database for terms which *begin* the exact same way (or which contain that exact substring somewhere within their text) than it is to find the spelling that the user *intended* based upon prior searches. That's a *lot* harder. To me, *that* is what "fuzzy matching" is.
This is real fuzzy matching, auto completion is nothing special
It's completion
Let's keep some perspective here on where these things go back to.
Not quite completion
Google search does appear to be 'just' completion, starting from the beginning, whereas Sublime Text picks up ad hoc elements from throughout the file/command name, which kind of covers misspellings.
Not sure about Ubuntu as I currently don't have a machine running it.