I think it might be different from country to country. I will give an answer how it is in Sweden.
When Oscar I died in 1859, his elder son, Crown Prince Carl, became King. Carl XV's younger brother Oscar was Heir Presumtive, but he was never Crown Prince, nor did he hold a special title showing that he was first in line of succession.
When Gustaf V died in 1950, his eldest son, Crown Prince Gustaf Adolf, acceded to the throne as King Gustaf VI Adolf. The new King's eldest son, Gustaf Adolf, had died in 1947, so the King's grandson Carl Gustaf became Crown Prince.
In 1973, King Gustaf VI Adolf died, and his grandson, the Crown Prince, acceded to the throne as King Carl XVI Gustaf. The new King had no son. Therefore, his uncle, Prince Bertil, became Heir Presumtive, but with no special title to show that he was first in line of succession. In 1979 the King became father to a son, who from birth was Crown Prince Carl Philip. In 1980 a change of the Act of Succession allowed for the eldest child regardless of gender, to inherit the throne. Thus, the King's daughter Victoria, who was born in 1977, became Crown Princess.