The House of Wettin is indeed a dynasty which contains other houses. There are a number of branches, sub branches, etc. The whole house is usually described as being of two branches: Ernestine and Albertine, with the Ernestine branch being senior to the Albertine branch.
The genealogical head of the Ernestine branch, and therefore of the entire House of Wettin, is the titular Grand Duke of Saxony, Prince Michael of Saxe-Weimar & Eisenach.
The next branches in order of seniority are the ducal houses of Saxe-Meiningen & Hildburghausen and Saxe-Coburg & Gotha.
The Coburg line, of course, genealogically includes the British Royal Family descending in the male line from Queen Victoria, the Belgian Royal Family descending in the male line from King Leopold I, and the Bulgarian Royal Family. These families have at various times had or have adopted other names but that doesn’t negate their membership in the Coburg branch of the House of Wettin.
The Albertine branch of the House of Wettin became the Saxon Royal Family. It is extant in the male line but a female-line descendant claims the headship in opposition to other members of the family. He is not a member of the House of Wettin.