When Is Emotion Not Affect?

When it is not used to enact the self or intersubjective relations through an interpersonal assessment. For example, the clause

She was surprised that the answer was thirteen

construes a process of emotion, but on its own, does not enact an appraisal, since nothing is assessed positively or negatively.

On the other hand, the clause

She was pleasantly surprised that the answer was thirteen

both

1. construes a process of emotion (was surprised), and 
2. enacts a positive appraisal of that emotion by reference to a Quality of emotion (pleasantly), and so constitutes an instance of affect.

Halliday & Matthiessen (1999: 7):

The ideational metafunction is concerned with construing experience — it is language as a theory of reality, as a resource for reflecting on the world. The interpersonal metafunction is concerned with enacting interpersonal relations through language, with the adoption and assignment of speech roles, with the negotiation of attitudes, and so on — it is language in the praxis of intersubjectivity, as a resource for interacting with others.