Someone told me that in order to receive a residence card, you need to submit an application for issuing/replacing a residence card. Is this the correct form?

NO. If you want to receive residence card, you must submit an application for a temporary residence permit. You submit the application for the replacement of the residence card when the data in the residence card you currently have has changed. If you have a temporary residence card that expires and you want to stay in Poland, submit an application for a temporary residence permit.