Do these have a separate cost?
sstore(1, 10) # first time adding a value to storage with this key
sstore(1, 20) # changing the value in storage.
I looked for a list of gas costs / opcodes, and the only one I could find (https://docs.google.com/spreadsheets/d/1m89CVujrQe5LAFJ8-YAUCcNK950dUzMQPMJBxRtGCqs/edit#gid=0) is a year old. It seems to say that modifying storage is cheaper, but I'm not sure if these values are outdated.
Best Answer
Yes, using storage has different gas costs:
The Yellow Paper is the underlying source.
EIP-2200 has further explanations.
Related question: Does an SSTORE where the new value is the same as the existing value cost gas?