The definition of a semi-professional boxer varies, depending upon the place and date.
For example, in Cuba, for years, an amateur was not allowed to become a professional or semi-professional if he could not prove that he had at least twenty fights in the unpaid ranks. The semi-pros were the novice fights of a boxer's otherwise professional career. Semi-pros got paid a purse. The only difference between pros and semi-pros was the level of experience. Four-round fighters were considered semi-pro, and very experienced four or six-round fighters were considered pros. They were considered professional boxers, but at a novice level. It was sort of a novice division within the pro system. Semi-pro fighters could not fight amateurs. And, as they had been paid for bouts in the past, they could not return to the amateur ranks. Cubans did not list the semi-pro bouts on their official fight records, although some managers padded the records by adding them. But the Cuban Boxing Commission officially did not include them.
Some older French boxing records appear to be a mixture of pro and semi-pro bouts.
In Spain, there is a "neo-professional" category, which may be similar to semi-professional.
Then there were the situations in California and Washington, USA, during the early 1900s (circa 1900-33). Early on, only truly amateur boxing was permitted, not professional prizefighting. Some promoters staged shows where they paid boxers to appear, but presented the bouts to the general public under an amateur license allowing boxing in private athletic clubs. For all purposes other than in name, these were professional fights. If questioned, the promoters would claim that the boxers were merely paid "training expenses." So many boxers fought both truly amateur bouts (particularly in tournaments) and pro (paid) bouts, back-and-forth, sometimes for years. Those boxers were the semi-professionals of their time and place.
Some career records here at BoxRec, therefore, may contain a mixture of the above variations of bouts.