how is the minus sign understood in set theory, is it similar to the complement (\) function. Assume:
$A = \{1,2,3\},$
$B = \{2,3,4\}$
Is $A - B = \{1\}$, or is it $\{1\}$ plus the piece of $\{4\}$ that you 'owe', assuming in Venn Diagram you are subtracting a piece of $B$ from $A$ itself that do not contain the element '4'. (Is it fair to visualise sets in Venn Diagrams?)
Or do we just equate the minus($-$) sign to the complement() function.

The symbols $-$ and $\setminus$ typically denote the same thing, namely relative complement (a.k.a. set difference):
$$A - B = A \setminus B = \{ x \mid x \in A \text{ and } x \not \in B \}$$
The other operation you mention is symmetric difference, often denoted $A \triangle B$, which is defined by
$$A \triangle B = (A \setminus B) \cup (B \setminus A)$$
or equivalently $A \triangle B = (A \cup B) \setminus (A \cap B)$; it is the set of objects which are elements exactly one of $A$ or $B$.
In your case, you have $\{ 1, 2, 3 \} \setminus \{ 2, 3, 4 \} = \{ 1 \}$ and $\{ 1, 2, 3 \} \triangle \{ 2, 3, 4 \} = \{ 1, 4 \}$.
