The definition of a semi-professional boxer varies, depending upon the jurisdiction.
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 twenty fights in the unpaid ranks. The semi-pros were the novice fights of an 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.
Then you have a situation which occurred in Washington State, USA, during the early 1930s, before professional boxing became legal in 1933. Boxers frequently got paid a purse, although the money was given the euphemism of "training expenses," and the bouts not always labelled as "professional." In Seattle during the early 1930s, the Austin and Bishop club held frequent "semi-amateur" shows--which featured pro fighters on what was called an "amateur" show. (These were not exhibition bouts.) The "professional" bouts are included in the boxers' official fight records, while the semi-amateur or amateur bouts have not.
And some older French boxing records appeared 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.