Active Ingredient:

If two drugs have the same active ingredient, does that mean they are relatively the same?

I understand there are certain advantages to different types of capsules, but other than that, am I getting the same basic thing? Could would still be superior to the other?

A simplistic answer is the ‘drug’ is what does the business once in your body, whilst what’s in the capsule could be any number of versions (‘prodrug’ sounds good, but it wouldn’t be universally correct), eg different salts, different physical formulation (eg particle size), a compound which is much more complicated than the drug, but releases the drug at some stage etc. The different forms will likely give different bioavailabilities. Hence the different forms are likely to give different doses of the drug, even though they contain comparable amounts of the drug.
Ideal formulations (for most situations) have been arrived at for most common and over the counter drugs, so there’s little to worry about from that point of view.