Machinery or vessels in general

Question

Machinery or vessels in general To the following question: “...without a mashgiach (or any competent supervisor for that matter), if items are made with kosher ingredients, but manufactured or processed on machinery or in plants where non-kosher products have been processed, etc., does that not pose any problems?” You answered: “... We never need to worry about the machines. One reason is that stam Keilim Ainum Beney Yomam” Does that mean that I can cook kosher food in a gentile’s pots? Or does this ONLY apply in packaged goods? If the answer is the latter, please, for my own edification, what is the halakhic distinction between packaged and non-packaged foods? Thanks