Barb Adapter 3/4" Barb x 1/2" Spigot , The Glue Side glues inside a 1/2" Fitting which would measure 3/4" and a 3/4" ID tube would be glued over the barb.
This part is a 3/4" Barb Adapter x 3/4" Slip / 1" Street.
The Glue Side glues inside a 1" Fitting (like a coupler) and the inside would fit a 3/4" connection.