Are iphone messages stored in the phone or in the card?

SMS in iPhone is stored in the phone memory, so you can still see SMS in the phone even if you change or take out the sim card.

IPhone does not support saving SMS to sim card.

Short Message Service (SMS for short) refers to the text or digital information directly sent or received by users through mobile phones or other telecommunication terminals. The number of characters that users can send and receive SMS at a time is 160 English or numeric characters or 70 Chinese characters.