The difference between GRE over IPsec and IPsec with crypto map is that GRE (Generic Routing Encapsulation) over IPsec can encapsulate and transport non-IP protocols across an IP network, whereas IPsec with crypto map is typically used for IP traffic. GRE tunnels wrapped in IPsec provide a way to transport multicast traffic and other protocol types across an IPsec VPN, offering greater flexibility in the types of traffic that can be secured.