It is hard to maintain a difference between the two words used here. The terms function in contexts of worshipping and serving the Lord. The fact that Zephaniah uses terms that are standard for the seeking of the Lord and negates them reiterates the apostasy that the preceding verses have highlighted. Zephaniah uses these common terms rhetorically to make his point that the people of Judah have become apostate.
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6 those who have turned back from following the LORD, who do not seek the LORD or inquire of him.”