Regarding the differences in apparently like creams, the first thing that comes to mind for me is pasteurization. Pasteurized cream will whip better and taste better than ultra-pasteurized cream.
From the Milwaukee Journal Sentinel:
There are two types of heavy whipping cream available at most supermarkets: pasteurized and ultra-pasteurized.
The two are not interchangeable in cooking. Pasteurized cream has been heated to 167 degrees for 15 seconds, then chilled. It has a shelf life of about 18 days.
Pasteurized cream tastes fresher and whips up quickly into stiff peaks. It separates easily into solids and buttermilk for butter-making.
Ultra-pasteurized cream has been heated to 280 degrees for two seconds and then chilled. This gives it a longer shelf life — up to 60 days, unopened. But it won't whip up as easily or hold peaks as long as standard pasteurized cream. Some creameries add stabilizers to their ultra-pasteurized cream to help it to whip up better, but it still may not reach stiff-peak stage.
Ultra-pasteurized cream has a "cooked" taste and won't separate easily into large curds and buttermilk for making butter (or cheese).
Standard pasteurized cream is becoming harder to find. Fewer creameries are making it, and more stores are stocking only ultra-pasteurized cream.
All ultra-pasteurized cream and milk must be labeled by law, so check cartons or bottles before you buy.
In the US, heavy whipping cream must have a fat content of at least 36%. Products labeled with the interchangeable terms light whipping cream or simply whipping cream must contain 30% to 35% fat.
From the University of Guelph, this is a quite interesting article (including diagrams) about what happens when you whip cream:
The structure of whipped cream is very similar to the fat and air structure that exists in ice cream. Cream is an emulsion with a fat content of 35-40%. When you whip a bowl of heavy cream, the agitation and the air bubbles that are added cause the fat globules to begin to partially coalesce in chains and clusters and adsorb to and spread around the air bubbles.
Regarding creams vs. other animal or vegetable fats, this article from MILKingredients.ca states:
Cream and other milk fat products (such as butter) are very different than fat from other animal and vegetable sources due to the presence of an aqueous phase, proteins and phospholipids. Milk fat exists in the form of globules dispersed in an aqueous phase of milk. Surrounding the fat globules is a membrane made up of varying proportions of protein, phospholipids and glycerides. The phospholipids in the membrane are of primary importance and account for much of the emulsifying properties of the fat globule membrane. The absorption of casein, proteins which are within the aqueous phase of cream, onto the milk fat globule surface when the globule membrane is disrupted (e.g. as a result of shear or homogenization), allows for production of variations in viscosity which can impart different functionality in food products. Caseins promote interaction with other molecules such as calcium, creating a new structure within the cream and therefore changing the textural properties.