For the broker it may be the same, since the actual act of recharacterization requires you to withdraw the money from one account and put it into the other. The specifics of withdrawing from Roth for re-characterization may be warranting a special procedure for them, but from Traditional to Roth - they're blind to whether it is conversion or re-characterization.
The one who's not blind to it is you. According to the IRS, in order to re-characterize, all you need is to do the conversion before the tax return due date (+ extensions), i.e.: before April 15th, or if you submitted the form 4868 in a timely manner, October 15th next year (after the year to which the deposit is attributed, so in your case - it is October 15th, 2014).
To recharacterize a contribution, you generally must have the
contribution transferred from the first IRA (the one to which it was
made) to the second IRA in a trustee-to-trustee transfer. If the
transfer is made by the due date (including extensions) for your tax
return for the tax year during which the contribution was made, you
can elect to treat the contribution as having been originally made to
the second IRA instead of to the first IRA. If you recharacterize your
contribution, you must do all three of the following.
Include in the transfer any net income allocable to the contribution. If there was a loss, the net income you must transfer
may be a negative amount.
Report the recharacterization on your tax return for the year during which the contribution was made.
Treat the contribution as having been made to the second IRA on the date that it was actually made to the first IRA.
You should ask the broker, however, to have the recharacterized amount to appear on the form 5498 for the new contribution.