The difference in usage between supper and dinner is whether or not to add a or the in front of them, and whether or not to add a when there is an adjective in front of them.

have supper / breakfast / dinner / supper This is true that there are no articles, you can remember them as fixed phrases, but if there are other words modifying the meal before or after the meal, then you need to use the articles. In your question, there is a prepositional phrase at mike's house as a postpositional determiner modifying dinner, so there are articles before dinner. Similarly, have a big supper have a quick breakfast have a big dinner have a quick breakfast do you understand? Hope to adopt~~~

dinner is usually interpreted in two ways, as a formal meal or a banquet (the more formal kind, where alcohol is drunk), either at noon or in the evening, as follows:

dinner: a formal meal of the day eaten at noon or in the evening

banquet: a formal banquet or a big feast held for someone or something.

Supper is dinner, the more casual kind (from the French 'soup'). Sometimes it also refers to a dinner party (a ball or set for dinner)

dinner and supper are two nouns that refer to dinner in English. dinner is often used to refer to the main meal of the day, which can be either dinner or lunch. In English-speaking countries, dinner is usually the richest meal of the day, so dinner is often used to refer to dinner. In addition, the word dinner is more formal and is often used to invite friends to a dinner party. In Scotland, supper can be used to make a simpler, later meal for ordinary people. supper is also fixed to refer to the last supper before the crucifixion of Jesus in the Bible - lord's supper or last supper.