Replacing font changes formatting

It certainly sounds like the fonts are different judging by the fact that you have to find and replace the font in the document at all. This shows that your version of the font and the version that the other person is using are not exactly the same. If they were then, assuming that the font is already open on your computer, the document would simply open with the font active and no need to replace it. You should also know that font makers periodically change their kerning and tracking tables which means that even if you buy your font from the same place but not at the same time it is possible that the font will handle kerning and tracking differently. As I understand it, in collecting a job for handing off to another party, it is legal to supply the collected version of your font as long as the recipient also has a licensed version of that font. This way the version of the font that was used to create the document can be used for output without unwanted reragging. Also if the font is from the Adobe Typekit aka Adobe Fonts then anyone who has access to those fonts through their Creative Cloud subscription can activate that font on their system. A physical copy of Typekit fonts can not be collected, however.