Definitions

'Moral Realism' is defined as the claim that some moral facts (states, properties, entities) exist.

'Objectivist' Moral Realism' is defined as the claim that moral facts (states, properties, entities) exist objectively. (This is meant to delimit the present position from 'subjectivist' moral realism, according to which moral entities can be there 'non-objectively', and some moral entities do.) 

“Egoistic” is not particularly defined here; but it is assumed that while someone’s intending to realise p may imply that she wants p, it does not follow that her intention is egoistic.

(In the following partial explications, I consistently aim at sufficient conditions only. 'Moral intention', 'moral action' and 'moral ought' are supposed to be terms/expressions/notions of normal natural English speakers.)

'Moral intention'. That an intention is non-egoistically directed at the creation of a valuable state means (i.e., is sufficient) that it is a ‘moral’ intention. 

'Moral action'. That an action achieves a moral intention means that it is a ‘moral’ action.

'Ought'. If someone can do x, and is aware that doing x would advance the occurrence of a valuable state (e.g., by advancing the non-occurrence of a dis-valuable state), then she ‘ought to do’ x. 

'Moral ought'. If someone ought to do something which is not subject of her egoistic will, this means that she ‘morally’ ought to do it. 

[‘(Morally) ought to do’ is meant in the other-things-unconsidered sense. You ought not to cause the suffering of an innocent being, other things unconsidered. At the same time, if a doctor needs to cause suffering in an innocent person for the sake of healing, then considering this fact, she perhaps ought to do so.]
 

'Moral fact'. If someone morally ought to do something, or performs a moral action, or has a moral intention, this is a ‘moral fact’. 

Moral state. The existence of a moral facts is a 'moral state'.