Is there any chance that anyone could clarify the difference between transport winged, walking, and dolphin symbol and the normal symbols. I know that there is the special transportation attack where you can use a move and attack and -2 attack from the person attacking. Is there any benefits as using them to carry someone? Do they not subtract the -2 for carrying someone, Or is there nothing special beside the special attack with a -2 attack?

The difference between and is the possesses the Move and Attack combat ability and the Carry ability.

The difference between and is the possesses the Move and Attack combat ability and the Carry ability (both posses the Swim ability).

The difference between the and is the possesses the Move and Attack combat ability (both possess the Flight ability Carry ability).

Unless stated otherwise, the Carry ability will always modify the speed value by -2. Being a transporter does not change this.

As you stated, the Move and Attack ability is just HSS with a -2 to attack, but don't forget that you can only use Move and Attack if you are given the power action when not adjacent to an opposing character.