Sealing Around Shower Drain Advise Needed

I am finishing up a remodel and the sub that did the showers left a gap about 1/8" or so around the drain grate ring. Is it better to grout around this or to caulk around this will a 100% silicone caulk. Or am I better off with a siliconized latex caulk? There is one spot that might be a big larger because of a chip in the tile! Please advise.
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Anytime when to dissimilar products meet it is better to caulk than use grout, The grout can break and crack to to expansion /contraction fo the materials or any movement between the two.
Use a caulk that is rated for use in baths and should be OK.

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