This one is short and easy. You know that this is a $D$-major chord:
X:1 L:1/4 K: C "D"[D^FA]
But so is this:
X:2 L:1/4 K:C "D"[^FAd]
The order of the notes does not matter. The only difference is the inversion. When the root of the chord is on the bottom, this is called the root position -- the chord isn't inverted. The chord is in first inversion is when the third (in this case $f\sharp$) is on the bottom, and in second inversion when the fifth (an $a$, here) is on the bottom.
X:3 L:1/4 K:C "Root position"[D^FA] | "First inversion"[^FAd] | "Second inversion"[Ad^f] |
In chord symbol notation these inversion can be specified with a slash followed by the precise note that should be on the bottom1. Like this:
X:3 L:1/4 K:C "D"[D^FA] | "D/F♯"[^FAd] | "D/A"[Ad^f] |
For clarity I left out some possible variations where the notes are not packed together as closely as possible. These positions are still named after which note is in the bottom spot according to the pattern I described. But their voicing is additionally said to be closed when the notes are packed and open when they are spread. This can't be specified using chord symbols alone.
X:3 L:1/4 K:C "Root position"[D^FA] [DA^f] | "First inversion"[^FAd] [^Fda] | "Second inversion"[Ad^f] [Ad'^f] | w: closed open closed open closed open
The designated bass note can in fact be any note, not just chord notes. I may discuss this in a future post.