I regularly copy content from one INDD file to another. They have the same paragraph styles and the same character styles. However, when I copy content from document A to document B, it consistently changes the font from Adobe Garamond Pro to Minion Pro. I can easily run Find Font to replace all instances of Minion Pro, but I'd prefer it copy correctly. Suggestions?
InDesign CC 2015.4 -- 11.4 -- x64
Have you tried pasting without selecting any paragraph or character styles in the document B.
Do you mean having the default character style and paragraph style set to [None] and [Basic paragraph], respectively? If so, yes.
Also, I made sure the default font in document B is set to Adobe Garamond Pro. If I choose Paste Without Formatting, the font works properly, but then I lose any character styles.
You say the styles are the same, but maybe they really aren't, especially if you've used "based on" styles in either file. When you move content from one file to another and there are styles or swatches involved with identical names, the definitions in the receiving document are always used even when there is a difference.