SVG files don't contain DPI information. When you're opening the SVG file directly or pasting it from the clipboard, because there's no DPI specified within the file, the vector is rendered at 72 DPI.
The new document in which you're pasting the SVG file is probably at a higher DPI. Either scale up the pasted vector to match the document's DPI or reduce the DPI of the document to 72 DPI.