DmMaj9 is D, F, A, C# and E. It keeps every note of and adds the .
DmMaj9 and both contain the 9th. The difference is the 7th: DmMaj9 uses , while uses the flat 7th.
Choose between them by the seventh under a held 9th. The minor 3rd remains in both chords.
Also written DmM9, Dm(maj9) or D-Δ9.

DmMaj9 in 3rd inversion puts C# in the bass instead of D, the 7th of the chord. The notes are the same; what changes is what the bass line does, which is most of why you would reach for it — it lets the lowest voice move by step where the root would have jumped.
One of DmMaj9’s 9 shapes does this:x-x-11-10-10-12
How you get to it. The turn that lands on DmMaj9 is to : the ii and the V of D minor, which is where a minor tonic is usually arrived at rather than simply begun on.
Hear it land:→→
Contains DmMaj9 and adds eleventh and flat thirteenth.
Contains DmMaj9 and adds eleventh and thirteenth.
The common shapes and the derived voicings come from different places, and both are explained in how this site is built.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.