Is it bribery or reinforcement? An age old question, spewed mostly by critics of behavior analysis. None-the-less, it is a valid question indeed. Basically, it comes down to timing. If you said to your son/daughter "today if we play nicely with each other at the park, we will go to get an ice cream afterwards"...that would be considered positive reinforcement (if it increased the desired behavior in the future). However, if you waited until your kids were fighting at the park and then said, "if you calm down and stop fighting we can get ice cream" ...that would be considered bribery (because the challenging behavior is dictating the reward).
Intrinsic vs Extrinsic Motivation
A Quantitative Review of Overjustification Effects in Persons with Intellectual and Developmental Disabilities (Levy, et al., 2016): "The overjustification hypothesis suggests that extrinsic rewards undermine intrinsic motivation. Extrinsic rewards are common in strengthening behavior in persons with intellectual and developmental disabilities; we examined overjustification effects in this context".
The Effect Of Token Rewards on "Intrinsic" Motivation for Doing Math (McGinnis, Friman, and Carlyon, 1999): Motivating children to do math can be difficult, and contingent token rewards are sometimes used to help. The large literature asserting a decremental effect of rewards on ‘‘intrinsic’’ motivation is especially critical of token rewards used with children (e.g., Kohn, 1993). Overall, the results [of the present study] are inconsistent with warnings about use of token rewards to motivate children.
Other People's Perspectives
To begin reading other people's perspectives on the matter, you can start here: