Rav Ashi says that the source for meat and milk being prohibited to eat and benefit from is the pasuk which says לא תאכל כל תועבה from which chazal darshen כל שתעבתי לך הרי הוא בבל תאכל. The gemara suggests that the same problem should apply to food cooked on shabbos, and it should be prohibited to eat and benefit from, but darshens from the pasuk of כי קדש היא לכם that ma'aseh shabbos is permitted. The gemara further tries to suggest that when one violates the prohibition of plowing with an ox and mule together or muzzling while working, the product should be forbidden. The gemara answers that since we permit ma'aseh shabbos, we should certainly permit the products of plowing with an ox and mule, or muzzling it while working. Rashi struggles with an obvious question, why wouldn't we also learn from ma'aseh shabbos that even bassar b'cholov should be permitted to derive benefit from. Rashi explains that there is a difference. When it comes to meat and milk, one is eating the actual issur that the Torah despised, whereas by ma'aseh shabbos and these other aveiros, we are merely speaking about the product of the issur, not the issur itself.
Tosasfos (end of d.h. choreish) struggles with why we consider the food cooked on shabbos to be merely the product of the aveira but not the תועבה itself, whereas by meat and milk we consider the food to be the actual תועבה that was despised by the Torah? Tosafos explains that it must have to do with how apparent the issur is within the item. By meat and milk where the issur is apparent in the product, the product of the aveira is considered the תועבה, but by ma'aseh shabbos where the issur isn't apparent in the product because one cannot tell from the product that it was cooked on shabbos, the food isn't considered the תועבה.
Tosafos approach seems to be using a d'rabbonon style logic to distinguish between bassar b'cholov and ma'aseh shabbos on a Torah level. It would seem difficult to say that appearance of the product would determine whether the Torah renders it a תועבה. The Rashash suggests another distinction to answer Tosafos question. The cooking of meat and milk is that act of prohibition that the Torah forbids, therefore the product of that act is considered a תועבה. But by ma'aseh shabbos the Torah doesn't forbid specifically the cooking of food, rather the Torah forbids any melacha to be done on shabbos. The food that is cooked on shabbos is not a direct product of what is specifically forbidden by the Torah, therefore not considered a תועבה.
I would like to suggest a slightly different approach. According to the approach that meat and milk that have been cooked together are forbidden to eat and benefit from because they are considered a תועבה due to the fact that an issur was done with them, it should only be forbidden if cooked by a Jewish adult. Had the cooking been done by a child or at least by a goy, where there was no violation in the process of cooking the product shouldn't be considered a תועבה. Yet, Rashi 114b writes that even if cooked by a goy or a child (rashi implies that we don't render an aveira done by a child to be a ma'aseh aveira), we would consider the product a תועבה. Rashi 114b explains that it is not the act of the aveira that renders the product a תועבה, rather the תועבה is the item itself. Rashi understands that it is as if the Torah would have said that meat and milk is a תועבה, therefore stay away from cooking it. When the Torah identifies an item and forbids an action associated with that item, it can be understood that the action doesn't cause the item to be forbidden, rather the torah recognizes the item as something despised herefore forbids the action i.e. cooking. This would only apply when there is a specific item referred to by the Torah such as meat and milk. The Torah considers meat and milk that is cooked together to be a תועבה, therefore forbids any Jew from cooking it. But, even if a goy were to cook it, the item is still a תועבה. In contrast to the issur of ma'aseh shabbos - the Torah doesn't despise the product, therefore forbid the action of cooking. If that were the case then even something cooked by a goy should be included. The fact that it is only considered ma'aseh shabbos when done by a Jew indicates that the action is what is considered forbidden, and the food is merely a product of the forbidden action to cook. This would not give the food a status of תועבה.