The Sages enacted two different forms of prohibitions against the foods of a gentile. One which relates to the bread of a gentile, and is called Pas Akum and the second which relates to the cooked foods of a gentile which is called Bishul Akum.
The Halachic differences between Pas Akum and Bishul Akum:
Pas Akum has a leniency that it suffices for a Jew to do any part of the baking process to permit the bread. By Bishul Akum however, according to some opinions one must actually place the pot on the fire, and it does not suffice to simply raise the flame. Likewise, Pas Akum contains a leniency when it is commercially made, as it is only a stringency not to eat it, while Bishul Akum is forbidden from the letter of the law even when cooked by a store. A leniency attributed to Bishul Akum over Pas Akum is the Bishul Akum only applies if the food is able to be served at a kings table. However Pas Akum is forbidden even if the bread cannot be served at a kings table.
Pas Akum or Bishul Akum: The prohibition of Pas Akum extends towards Mezonos products. Nevertheless, the Poskim explain that this only applies towards Mezonos products that can become Hamotzi upon setting a meal over them, while other Mezonos products do not retain a Pas Akum prohibition, although do retain a Bishul Akum prohibition. Those Mezonos products which are forbidden due to Pas Akum are not forbidden due to Bishul Akum and hence retain all the leniencies and stringencies attributed to Pas Akum, as explained in the introduction of this chapter. Other Mezonos products however receive all the leniencies and stringencies of Bishul Akum.
Mezonos foods which can become Hamotzi: All baked Mezonos products that are made from one of the five grains, and require a Hamotzi and Birchas Hamazon if one were to set a meal over them, fall under the prohibition of Pas Akum and not Bishul Akum. These products receive all the leniencies [and stringencies] attributed to Pas Akum, and hence in those places that are accustomed to be lenient to eat Pas Akum [of a gentile bakery] may do so by these products as well [so long as their ingredients are certified as Kosher, and so long as they are not filled with foods that contain a prohibition of Bishul Akum]. A Mezonos food can only become Hamotzi upon setting a meal over it if it is made of dough that is baked, such as Pas Haba Bekisnin, as explained in Orach Chaim chapter 168 regarding the laws of blessings.
Mezonos foods which can not become Hamoitzi: All Mezonos products that remain Mezonos even if one were to set a meal over them, do not fall under the category of Pas Akum but rather of Bishul Akum. The laws of Bishul Akum will be explained in the next chapter. A Mezonos food always remains Mezonos even upon setting a meal over it if it is a cooked product, such as cooked dough, or is baked into a very thin batter, as explained in Orach Chaim chapter 168 regarding the laws of blessings.
All baked Mezonos products that can become Hamotzi upon setting a meal over it fall under the prohibition of Pas Akum, both for leniency and stringency. All Mezonos products that can never become Hamotzi fall under the prohibition of Bishul Akum, both for leniency and stringency
List of foods included in Pas Akum:
Baked pastries that do not contain stuffing’s of other foods fall under the prohibition of Pas Akum and not Bishul Akum. Thus, those that are accustomed to eat Pas Akum bakery products, may eat these products made by a gentile baker, so long as their ingredients are certified as Kosher.
Sufganiyot are deep fried and hence fall under the prohibition of Bishul Akum and not Pas Akum. Thus, Kashrus agencies must insure that their Sufganiyot follow the standards required for Bishul Yisrael, such as having a Jew light the flame or [according to the Sefaradim] enter the Sufganiyot into the oil.
Are pastries and casserols that are stuffed with food forbidden due to Bishul Akum?
Although all Mezonos products that can become Hamotzi are under the laws of Pas Akum, nevertheless if the Mezonos contains stuffing of food, then those foods receive so long as they are not filled with foods that contain a prohibition of Bishul Akum].
 Peri Megadim 112 M”Z 3; However the Avnei neizer holds that in such a case it too is permitted, as brought in Q&A 2A!
 Rama 112:6 regarding pastries such as honey cake and Kichlich; Michaber 112:6 regarding the Infanda:Pashtida, however to note that the Infanda is Hamotzi if made from real dough.
 Taz 112:6; Shach 112:18; Toras Chatas 75:12; Beis Yosef 12 in name of Rav Yechiel; Peri Chadash 112:17; Beis Lechem Yehuda 112:11; Kaf Hachaim 112:35; See Hakashrus 19:2
 Taz 112:6 based on Rama 112:6 which mentions that Lekach and other sweet pastries have a prohibition of Pas Akum; Shach 112:18; Toras Chatas 75:12; Beis Yosef 12 in name of Rav Yechiel; Peri Chadash 112:17; Beis Lechem Yehuda 112:11; Kaf hachaim 112:35; See Hakashrus 19:2
 Such as that even if they are unfit for a kings table, it is forbidden.
 See Q&A
 See also Seder Birchas Hanehnin chapter 2
 Based on Poskim above; Rivash 28; Peri Chadash 112:17; Beis Lechem Yehuda 112:14; Kaf Hachaim 112:36
 Shach 112:17; Beir Heiytiv 112:9; Rivash 28; Peri Chadash 112:17; Beis Lechem Yehuda 112:14; Kaf Hachaim 112:36; See however in Sefer Hakashrus 19 footnote 14 that R. Moshe Shternbuch in Teshuvos Vehanhagos 3:248 rules Mezonos foods that are baked very thin can be considered Pas Akum and not Bishul Akum.
 See also Seder Birchas Hanehnin chapter 2
 Birkeiy Yosef 112 Shiyurei Bracha 9; Kaf Hachaim 112:38
 Rivash 28; Peri Chadash 112:17; Beis Lechem Yehuda 112:14; Birkeiy Yosef 112:11; Kaf Hachaim 112:36 and 43; Sefer Hakashrus 19 footnote 14
 Birkeiy Yosef ibid; Kaf Hachiam 112:43; See Yechaveh Daas 5:53