parallax is always to be added in the case of the sun.
"Lectures in Navigation"
Ernest Gallaudet Draper
The distance of a star is equal to the radius of the earth's orbit divided by the parallax, in seconds of arc, and multiplied by the number 206265. A weak point of this method of measuring stellar distances is that it always gives what is called a relative parallax-i.
"A Text-Book of Astronomy"
George C. Comstock
No one has ever succeeded in measuring the parallax of a nebula or star cluster.
"A Text-Book of Astronomy"
George C. Comstock