If you are talking about two InDesign documents, it is because there is a paragraph and/or character style applied to the text, and that style has different definitions in the two documents.
Check to see what styles are applied, and then use Break Link to Style before copying the text. This will prevent the new document from reformatting the text according to its version of the styles.
Break Link to Style? Can this be handled for multiple styles and both Paragraph & Character Styles simultaniously?
Once for paragraph style and once for character style (if there is one). You can select several text boxes at once and do this.
--One note: if there are nested styles, the character styles used in those will remain.
Another option for keeping the styles intact would be to use Load Styles from within the new document, and move the styles from the old document over (using Override existing)