HDMI and DP do not carry their signals in the same way. HDMI/DVI use a pixel clock and one wire pair per colour, whereas DP is packet-based.
"DisplayPort++" is the branding for a DP port that can pretend to be an HDMI or DVI port, so an adapter or cable can convert between the two just by rearranging the pins.
To go from pure DisplayPort to HDMI, or to go from an HDMI source to a DP monitor, you need an 'active' adapter, which decodes and re-encodes the signal. These are bigger and sometimes require external power.