You should not be responsible for website security if you don't understand the absolute basics of SSL certificates.
It would be helpful if the CA (or reseller) confirmed (dispay a warning) that you really want to reissue with the same private key and explain the implications of doing so.
When reissuing a certificate the default behaviour should be to revoke the old one after some specified time has elapsed - that is what reissuing is for and what distinguishes it from simply buying a new certificate.