No. The two memory card slots on the Nintendo GameCube (Slot A on left, Slot B on right) are functionally identical. There is no hardware or software difference.
Slot A is often used by default if the game auto-selects, simply because it's the first port checked. Some users prefer Slot A for their primary card and Slot B for backups/transfer, but this is personal organization, not a system requirement.
To copy saves between cards: Insert both -> System Menu (no disc) -> Memory Card Screen -> Select file -> Copy -> Choose destination slot. Works regardless of which card is in Slot A or B.