It does not make sense to talk about dependence of populations. You need to ask yourself: "if I take item #1 from sample set #1, can I find an item in sample #1 to which it has a real relationship, i.e., can two such items logically be paired?"
Example: say, you own a pizza shop and you decide to change your recipe. You take 10 customers and ask each of them to rate your old-style pizzas and the, ask the same 10 people, to rate the new pizzas. Then you can match these two sample sets into pairs, because they involve the same people: Sarah's score for old-style forms a pair with Sarah's score for the new pizzas.
This is when you will apply a paired-sample t-test (for average scores).
However, if you asked 10 (or other number) DIFFERENT people after changing the recipe, the score of John for old-style pizza cannot be related to any of the new-style scores, because John is not part of the new scores. More strongly, if at least one of the person in the survey has been added/deleted/exchanged, you cannot have 10 matching pairs of scores anymore, hence you cannot apply paired-sample t-test, but you must recourse to an independent-samples t-test.
While independent-samples test can always be applied, it gives slightly larger uncertainties (larger p-value) than matching-pairs test, so you should apply the latter whenever it is feasible.