Tag and branch are the same from the point of view of svn server. They are both the "copy" operation (this is why they use the same menu item in TortoiseSVN, they are actually the "svn copy" command). Copy operation of svn server will create a link to original revision. So create tag or branch will not double the disk space usage. The disk space usage is actually related with how many files are modified based on a specific revision.
What is the difference of tag and branch? When you create a "tag", you mean you will save this link at a "baseline area" where it's prohibited to do checkout-modify-checkin operation. On the contrary, if you create a "branch", you will do checkout-modify-checkin operation in the future for new feature development or bug fix.
Use "svn help copy" for explanations.