@Gargron
I'd also rather call the first "happy smile" or "happy grin" or "happy laughter", and the latter just "smile" or "smiling face".
With these two:
🙁 Slightly Frowning Face
☚ī¸ Frowning Face
the "slightly" actually makes some sense.

😑 "Expressionless Face" is another that bothers me, as to me it looks more like an annoyed face than an expressionless one. Actually, it's the face I'm probably making while looking at the two emoji from your post and their descriptions.