\$ vs. ($)

Ralph asked,

| Philip, is there any difference in efficiency between \$? and ($)?.  Do
| they mean the same thing?

Philip has answered that they mean the same thing (one newline or nothing) if
there is $-interpretation going on.  However, if there is no $-interpretation
on the condition, then \$? means one literal dollar sign or nothing, and ($)?
means one newline or nothing.