Dual-port (more often called true dual port) has two read/write ports. Each port can be used for reading, writing, or both.
Simple dual-port has one read port and one write port. This often means that you can have wider data buses or lower resource usage (eg. a single 18K block RAM can go up to 18-bit ports in true dual-port mode, but in simple dual-port mode you can have 36-bit ports). The disadvantage, of course, is that you can't write to or read from multiple locations simultaneously.