Agar is a vegetable product harvested from seaweed. There are quite a few grades but generally speaking any agar available for cooking is suitable. It is primarily used by the cook as a gelling agent like gelatin. The selection of one over the other maybe the obvious choice of a vegetable product vs an animal product.

It can be used for gelling acid foods such as acidic fruit juices whereas gelatin is likely to fail. The amount needed is less in quantity generally speaking this is of little consequence.

It will remain gelled above 30ºC (86 F) whereas gelatin liquefies at this temperature and is unsuitable for presenting warm foods in a gelled matrix. This is also a very good thing to remember for outside dining on hot days. Jellies and aspics may start to liquefy if made with gelatin but agar gels will remain firm. Gelatin on the other hand gives a smoother texture the agar texture can be mitigated to a small extent by using the minimum amount possible of the agar-agar. Agar has a distinctive bite or give compared to gelatin because the gelatin is beginning to soften already in the mouth as well as its structure. Any cooks' tricks on this issue will be gladly accepted.

The preparation is a little different. Gelatin gels, as mentioned, liquefy at approx 30ºC (86 F)and return to a gel phase below this temperature. Agar is quite different in relation to temperatures. Solutions of agar will begin to gel at about 40ºC but won't liquefy until the temperature is raised to ~90ºC (194 F), very close to the temperature of boiling water.

To make a solution of Agar you need to boil the liquid and add the agar material maintain boiling for a further 5 minutes after solution. You can make a concentrated solution using a little of the liquid used within the recipe, generally water, but not necessarily so. Then you need to have the rest of the ingredients at about 40ºC (104 F) or above before adding the concentrated agar solution. Mix well at this stage and when this is complete you can allow the temperature to reduce. Your gel will then be formed and stable and it won't liquefy until the temperature is brought back to approximately 90ºC (194 F). Not something that is likely in a food presentation situation for such foods.

To prepare gelatin solutions you need water hotter than 30ºC (86 F) generally as hot as you can bear and add the gelatin material stirring until it dissolves. Some like to hydrate the gelatin material in cold water first, then raise the temperature 10 minutes later to effect solubilisation of the gelatin. The gelatin concentrate can be added to the dish in preparation keeping the temperature above 30ºC (86 F) until prepared. The food made with gelatin must also be kept at a temperature below ~30ºC (86 F)so as to prevent liquefaction.

Gelatin is solubilised collagen from skin, hides and bone of the animal whereas Agar is a vegetable origin carbohydrate and classed as a soluble fibre with all that nutritional benefit of soluble fibre. Agar granules or pure substance  can swell up to many times its dry weight with added moisture (generally the water in foods and drinks consumed) and has been used as a dietary aid for some time in European communities. It is marketed by some for this purpose in English speaking countries in relatively recent times.

Gelatin and gelatine are words used interchangeably. Gelatine is the common spelling for Commonwealth countries and I think evolved from a brand name of a commercial culinary gelatin(?). Both agar-agar and gelatin have many more uses both in other industries and in the food industry. They're both extremely valuable products. For instance the movie industry has used gelatin emulsion on the celluloid for the medium of the film material, I think for nearly a century. Other materials had been used but gelatin won out in  history because of stability, availability and cost. Agar-agar and its derivatives have become extremely important in purification of protein materials both in research and in production. It is being used to help heal ulcerated sores in patients afflicted and in recent times morphine has been incorporated into the agar gel and applied to the ulcers with remarkable pain control. The agar material has the ability to remove the ulcerated dead tissue  away reducing infection from the site keeping it clean and removing the inhibitors to healing that previously required very painful cleaning procedures at least once a day. Now this can be done almost painlessly at the patients bed.