てき/的 is originally from the transliteration of the English suffix "-tic", and changes the preceding noun to a na-adjective that expresses "having those characteristics", "regarding that" or "those kinds of manners". Thus, those two groups are different in meaning. For instance, 経済的な車 means "economic/economy car (reasonable price or good fuel-efficiency)" whereas 経済の車 doesn't make much sense.
Japanese people's way(s) of thinking
Japanese people-like way(s) of thinking
(They can be non-Japanese.)
an event in politics (e.g. election)
an even that has a political nuance (e.g. a meeting a political group gives support to)
The difference is sometimes huge. For instance, 人間的な can have a nuance of "humane/humanitarian", so 人間的な行動 means "sympathetic/moral/ethic action". On the other hand, 人間の行動 is just "action of people/human-being". Similarly, 文化的な and 経済的な can mean "civilized" and "reasonable/economically efficient", respectively, which 文化の and 経済の don't have.
You can see the difference in meaning in the example sentences in dictionaries or the real usages you'll come across. Concrete examples are often helpful for understanding rather than a comprehensive explanation.