Usually, the scheme of a scientific study has a hourglass shape scheme, from wide, to narrow, and wide again.
In the first wide, we use the introduction to describe the general topography and bring focus to a particular problem. Then we narrow down to describe how our experiment is designed, data are collected, analysis is done, etc.
When results are ready, we interpret them, and then again widen up the scope to talk about implications, applications, and recommendations in the Discussion section.
In my opinion, objectives are a list of actions to perform, or questions to answer so that you can complete the narrow part of the study scheme. Contributions are a list of applications or significance to other researchers that brought about by your work, and they are perhaps more fitting in the second wider part of the study scheme.
For instance, the objective of a project could be "to validate a low cost blood glucose measurement device." And if it is indeed valid, the contribution could be "allow more people to afford to measure their glucose, and potentially lead to better diabetes control in the population."