Chlorine is basically the only thing (not sure about baquacil?) thing that "cleans" (sanitizes) your pool. What they are asking, is which products are you using to chlorinate your pool? Are you using bleach? Are you using a powder (granules) of some kind? Are you using those chlorine "pucks"? Knowing which product your using is important, it will let the people who are trying to help you know what else is being added to your pool besides the chlorine itself.
The biggest issue is those pucks and sometimes powders contain stabilizer (known as CYA). It's not good to have a consistent rising level of CYA in the pool. You want to keep all of your pool chemistry in a target "range". Those pucks will push your CYA levels quickly too high, and no matter how much chlorine you add, your still going to have algae in the water. The other normally bad thing is calcium. Too much calcium makes the water very hard. If your using a "Cal-Hypo" product (calcium hyopchlorite) then your water hardness is going to start to climb too high. Both are problems that normally result in needed to drain half or more of your pool and refilling with fresh water.
Baking soda does not clear algae. It increases your total alkalinity. It affects the "pH" range of your pool. Having a total alkalinity level too high or too low is bad.
Pool store employees can be poorly trained and not really knowledgeable about pool water chemistry. The people testing your water may know only how to run the machine, and take what it say as gospel truth. It creates a "report" of which products you need to buy. They run the test, give you the report, and try to sell you whatever is on the list.
EDIT: I'll say that this is "generally" the case. There very well may be some great mom and pop pool stores out there where they really understand pool chemistry and really do know the in's and out's of taking care of a pool. I would venture these are few and far between... so as unfair as it is, it's safe to assume the store your going to is one that really has no clue. They "trust the machine" and whatever it tells them to tell you to buy. I support this conclusion, IF, they are the ones who told you to add baking soda to get rid of the algae.
Some times they don't even really ask the important questions. Like how you were previously caring for the pool, or if you have a vinyl liner or not, or if your using a salt water system or not. They just run the machine, the machine does the thinking, and they do the selling. Not a good way to do things. The pool store results can also be wildly inaccurate if the machine isn't properly and regularly calibrated.
