Any citizen can make an arrest for a felony or breach of peace committed in their view. It is called a citizens arrest. So Yes a bond enforcement agent CAN arrest.
If someone "detains" and you do not believe you are free to leave, you are arrested. You can be temporarily detained during an investigation, it is not an arrest as long as it is temporary. There is a fine line, as a uniformed officer has an air of authority.
This is a more complicated than would seem.
A detention is technically not an arrest. If you put cuffs on someone and put them in the back of a car, is that a detention? Most would say that is an arrest, but it depends on the circumstances.
When a bond agent puts cuffs on someone and places them in the back of a car for transport to jail, is that a detention? According to you it is and you are technically correct. However, they are not temporarily detained, they are going to jail. remember, they may not be turning that person over to local authorities, they are going to transport them to the county jail where the bond was set, which could be hours away. Of course, it could be in the same town, but they are going to take them to the county jail, not turn them over to the municipal police (likely).
So, you can call it a detention if it makes you feel like you've won. By all means. But ask most people this: if someone places you in handcuffs on an outstanding warrant and takes you to jail, have you been arrested?