Agar Agar is something used to make a sauce thicker so you can pour it over your food like meat, vegetables or desserts. Agar agar comes from gelatin source in the sea. Most Asians use it for cooking. More popular there than in other countries.
You mix Agar Agar with water and stir to make a paste..then add it to the rest of the ingredients...cook it and the heat makes it become thick.
You can mix agar agar with chicken broth and it will become thick for egg drop soup or anything you need thickened.
Cornstarch, wheat flour and rice flour are also used in the same way.
Puding I think you meant PUDDING...is usually made with eggs, milk, sugar and flavoring like vanilla for vanilla pudding and some thickener like agar agar, cornstarch or flours.
The PUDDING...is cooked over the fire in a double boiler which is one pot of water that has another pot sitting on top of it. The bottom pot hold the water and comes to a boil then the top pot hold the PUDDING ingredients...eggs, milk , sugar, flavorings like vanilla keep the water at a soft boil slow.so the pudding mixture does not burn ....you constantly stir it until it gets thick and then you pour it into little cups and chill it in the refrigerator before eating. Sprinkle some grated nutmeg on vanilla puddings it gives it a great taste. There is another word also for Pudding it's called "custard" ....they are both the same. some people cook it in a water bath in the oven and not on top of the stove....after mixing the ingredients it's poured into little cups and placed in a big long pan then the cups are placed in there and hot water poured all around these cups up to 1/2 way. Then it's baked in the oven until done.
Best luck in the kitchen...
Mama Jazzy Geri