Re: how to call these notes?

[David Rogers]

Appoggiatura is a term in composition for a particular kind of note
that doesn't belong to the harmony.
Acciaccatura ("crushed") is a playing technique that composers can request.

Neither one is really the name of this little note.

The little note isn't stroked OUT, because "stroked out" would mean
"disregard". It does have a stroke through it, just the word "out" is
not the best.
Appoggiaturas are very often notated with the little note *with* the
stroke through it, especially in older scores. ("Appoggiaturas don't
have strokes through them" is a modern rule that very often doesn't
apply.) Acciaccaturas have the stroke-through notation almost all the
time.

I have heard, but have no reference to back it up, that the stroke
through an 8th-note stem was once simply another way to write a
sixteenth note.

-- 
David