As I understand it, a font is a bit special, copyright wise. You only need to change it in very minor details to call it a completeley new font. See Arial vs. Helvetica.
That's right, if I recall correctly. You can't copyright a font. You can rip off an existing font and create a new one that looks strikingly similar, even visually identical. However, if you do that by reverse-engineering the font (e.g. extract the bezier curve out of the TTF) then it is illegal. There is a court case where Adobe (?) sued some ripoff (and won), with the argument that while you cannot copyright the font, the "program" that implements the font is still copyrightable. IANAL and my wordings and details may not be 100% correct, so please feel free to correct me.
On the other hand, I wonder... if I take an existing font. Print it to a very high resolution PNG (not vector graphic so all Bezier curves are lost), and use some font creation software that recreate the font by doing an approximation... whether this is still consider a copyright infringement. Just curious...
On the contrary; change is the word you must avoid at all costs. Change almost implies that there also is an unchanged part, and that would run the risk of copyright infringement (if the remaining part is small, it might be fair use). What you can do is design a font that is extremely similar to an existing one. And that is different (unique?) for font designs; for instance, you would have a hard time getting away with designing a cartoon character from scratch that is extremely similar to Mickey Mouse.
Arial isn't Helvetica tweaked. It's a fairly similar font squashed so that it's metrically compatible (i.e. you can swap one for the other and if you squint from a distance it'll mostly look the same as the characters have the same dimensions).
There's an interesting story behind Arial; it was developed as part of a PostScript clone back in the days of Adobe's tight control over the Type 1 specification. Microsoft then threw gasoline on the Arial fire by bundling it into Windows 3.1, purportedly to save licensing costs.