To be honest, I have used neither of these APIs, so can't comment on specifics. However, from what I know about the ESRI Geodatabase Framework and the developments that have taken place, I doubt there is any real "transition" path from the ArcSDE Java API to the ArcGIS Runtime SDK for Java. These are two completely different products, based on different technology. The Runtime API is not an evolution of the ArcSDE API.
So I think your best bet is a careful study of the ArcGIS Runtime SDK for Java API Reference documentation, and trying to find "equivalents" in there.
To be honest, I have used neither of these APIs, so can't comment on specifics. However, from what I know about the ESRI Geodatabase Framework and the developments that have taken place, I doubt there is any real "transition" path from the ArcSDE Java API to the ArcGIS Runtime SDK for Java. These are two completely different products, based on different technology. The Runtime API is not an evolution of the ArcSDE API.
So I think your best bet is a careful study of the ArcGIS Runtime SDK for Java API Reference documentation, and trying to find "equivalents" in there.