I don't believe there's any consistent definition in practice. In strict terms, 'analysis' is calculating the consequences and frequency of possible events, and 'assessment' is then comparing your analysis with a defined acceptance standard. But, unless you are into very detailed quantified risk assessment (QRA), it's rare to separate out the 'analysis' within the overall risk assessment.

But for QRA, specialist software is available to estimate both the consequences (e.g. how large & hot the fire from an ignited leak would be) and how likely that size of leak is. Because it's specialist work, the 'analysis' may be carried out by software experts, but the 'owner' of the risk then has to judge its acceptability - so that might be a reason for separating the two?

In my experience, once the overall assessment is complete (including hazard identification, risk analysis, acceptance criteria, and deciding what additional controls are feasible/ needed), then communicating the results is part of 'risk management', not 'analysis'.