There are many different strains of yeast (with, like you said, different codes and names). This is not just marketing; there are MANY possible differences between two strains.
First off, beer yeast can be separated most easily into two families; ale yeasts and lager yeasts. There are many biological differences, but the most significant to a brewer is the ideal temperature range and the rate of fermentation. Ale yeasts ferment best in the 60 - 70 degree range and are comparatively fast acting, while lager yeasts are best suited for lower temps (<55 F) and take longer to consume sugars. MOST homebrewers gravitate more towards ales than lagers for various reasons, although you'll find brewers of both here.
Within the two different yeast families, there are also two main FORMS of beer yeast; dry yeast and liquid yeast. There is a larger variety of liquid yeasts available, although both liquid and dry have their merits.
Between two different strains within the same family (two different ale yeasts for instance), the biggest differences you'll find are...
- Flavor profile; some give off unique flavors (fruitiness, phenols, esters, diacetyl, etc.), while others are known for being very "clean"
- Tolerance to alcohol content; some yeast strains are better suited for high gravity beers, while others will slow way down or even stop fermentation once the alcohol content of the beer reaches a certain level.
- Fermentation temperature tolerance; different yeast strains have different ideal temperature ranges. Some ale yeasts are tolerant of low fermentation temperatures. Others will provide a clean flavor profile even at higher temperatures.
- Attenuation; this is a measure of how much of the fermentable sugar is actually consumed and converted to alcohol/CO2 by the yeast. A low attenuation yeast will leave a maltier, sweeter beer. High attenuation yeasts leave a drier beer.
- Flocculation; this represents how easily the yeast falls out of suspension, typically after the sugar content of the beer has gone down.
There are more, but off the top of my head those are the biggest differences between different strains.
In regards to your question about the food supplement; no, don't use that for your beer. There is a very strong likelihood that you would be very disappointed with the results for a multitude of reasons. Without knowing all of the details of the processing used on yeast designed as a nutritional supplement, there's a strong likelihood that the yeast wouldn't even ferment. If it DID, there's no telling what you would end up with, but I somehow doubt it would be desirable.
Starting out I would recommend finding a dry yeast, like Fermentis Safale US-05 Dry Ale Yeast (Formerly US-56).
Austin Homebrew Supply