Should IRRs and HRs always be equal?

[Pure_Stats]

I am running an analysis in a large population registry where individuals enter and leave the dataset at different time points.

When i estimated the IRR between two distinct groups and a health outcome, and then a HR, I am finding a small difference (IRR 2.18, HR 2.01).

Shouldn't they have been identical, since I am not adjusting for any covariates, etc? Are there any reasons that could explain why they are not identical?

Any thoughts would be appreciated.

 

[hlsmith]

IRR??
HR??

Incidence Relative Rate
Hazard Ratio

If so, I would imagine not, since they are different models and likely use different distributions and HR addresses time to event. So I think even if follow-up was equal, they may still differ.