Are one type of rechargeable batteries interchangeable with other types of rechargables? Specifically, I was wondering about replacing NiCds with NiMh or some other type in solar lights.

No. The methods of determining when charging is complete and the method of charing is different. Each battery chemistry has different characteristics as well.

The battery charger must match the battery... as mentioned by KISS

Many items work with either NiCDs or NiMH batteries. Check with the manufacturer for your specific application.

Some chargers are autosensing and carry the price tag. When I changed out the 12V batteries in the boat from lead/acid to gell cell, the charger had to be replaced. The new $300 20A, dual battery charger will automatically sense the battery type.