Is it ethical/acceptable to give a lighter penalty to students who admit to cheating?
TL; DR: We adjust the penalty.

I sit on my department's Academic Misconduct Committee so unfortunately I see a lot of these cases. The University policy has created two similarly sounding, but different terms: academic misconduct and poor academic practice, with academic misconduct being much more severe than poor academic practice. Every student suspected of having engaged in poor academic practice is called into a meeting with the Academic Misconduct Committee. This committee looks at the evidence supporting academic misconduct/poor practice and hears the student's case which generally includes what training they have had about good academic practice, how the incident happened, and any evidence of extenuating circumstances (e.g., death in the family). 

Based on this process we can come to one of 3 decisions: 


not poor academic practice, 
poor academic practice, 
academic misconduct. 


If we decide that they did not engage in poor academic practice, the incident is essentially purged from the system. If the student is called in again in the future, we do not nominally know that they had been called in before. If we decide that it was poor academic practice, the students are warned and it is documented. We are not allowed to apply formal penalties in the case of poor academic practice. If they are called in again we know from the documentation and are unlikely to give them the benefit of the doubt a second time.

If we decide that academic misconduct has occurred we can apply one of a number of different penalties to the work: no reduction of the mark, remark the work with the offending material removed or reduce the mark commensurate with the misconduct (anywhere from a 5% penalty to a 0 for the piece of work). A second incident of academic misconduct results in the penalty being decided on by a university panel and starts with a zero for the class and can go as high as a zero for the year. In this way there is a big difference between poor academic practice and academic misconduct with no reduction in the mark since poor academic practice does not count as a first offense.

Within this framework the committee is faced with how to handle the students who admit the issue and the ones who deny the issue. Those who argue they didn't cheat and have no explanation as to how their assignment matches another's work are almost always found guilty of academic misconduct since they are not willing to help us create a case for poor academic practice. More often than not they receive a 0 since we have no evidence that mitigates the penalty. For students who admit what they did, we often consider poor academic practice as an outcome since they describe what they did and realize it was wrong. Sometimes the offense is too blatant to let off without a reduction, but generally saying what you did wrong and how you will not let it happen again reduces the penalty.