No, paying delinquent taxes does not mean you’ve purchased a property. Purchasing a tax lien is an investment that does not convey ownership to the lien holder.
The tax deed process does convey ownership. If the property for which a lien buyer purchased a tax sale certificate at a county tax sale is not redeemed during redemption period, the lien buyer must comply with additional statutory requirements in order to obtain a tax deed. You should consult an attorney regarding these requirements under Indiana’s tax sale statutes.