> CRDT's are about sharing data, whereas this CALM theory is only talking about making a local decision.

Both CRDT and CALM are about sharing data to make a local decision which is globally consistent.

Both use an order relation over datasets to modelise the concept of "adding more info to some partial input or output".

I would say that the difference is on their focus. CALM determines the frontier where no coordination is required and provides general criteria (no need either to retract former output nor to hear everything there is to hear nor to know all the participants). CDRT provides a mean to meet this criteria. By taking the least upper bound of former partial results, CDRT ensures that the outcome is growing.