The laws pertaining to Bishul Yisrael (food cooked by a Jew), are much more stringent than those for Path Yisrael (baked goods made by a Jew). There is also a difference between Sephardim and Ashkenazim, with Sephardim following a substantially stricter approach.
Foods that require Bishul Yisrael, require the participation of a Jew in the cooking process, without which they are forbidden. This holds true even if they were cooked in the utensils of a Jew in a Jewish home. There are two reasons for this enactment of the Hakhamim (sages). One is that they were concerned about the possibility of forbidden relations and intermarriage. Another reason is due to the concern that one might come to eat food that was not Kasher.
Not all foods are required to be Bishul Yisrael. Anything that is regularly eaten raw is exempt from the requirements of Bishul Yisrael if it is cooked. In addition, it must be the type of food that has some importance attached to it. Specifically, it must be the kind of food that would be served at a king's royal banquet or a banquet of one of his ministers. Food that does not fall into this category may be eaten without the participation of a Jew in the cooking process, (provided one knows that the food is Kasher in other respects).
(See Yoreh De'ah, 113:1. Ben Ish Hai, 2nd year, Parashath Huqqath, Oth 9)
Adding to R. Menashe's remarks:
What are two main differences between Ashkenazi and Sephardi kashrut?
One: The Ashkenazi need only light the fire; the Sefardi also must have a hand in preparing the food. theory, while an Ashkenazi can eat in any restaurant that has a legitimate certificate of kashrut, the Sefardi must check both for a certificate AND assurance that a Jew participated in the food preparation.
Two: For meats, an Ashkenazi accepts "glat" while the Sefardi requires Bet Yosef/Halak.
In theory, while an Ashkenazi can eat in any restaurant that has a legitimate certificate of kashrut, the Sefardi must check for a certificate, assurance that a Jew participated in the food preparation, and that the meat is Bet Yosef/Halak.
