Difference between active HDMI signal to Display Port signal conversion and passive of the same?

An "active" adapter transfers connector and protocol, while a "passive" adapter just changes the connector. Most active adapters work just one way, but they are the most reliable when used correctly. So I would search for an "active" HDMI to DisplayPort adapter and buy a DisplayPort cable because your current hdmi cable will not fit.

There's no passive HDMI to DP adapter, but only DP to HDMI one, which requires the source itself to be able to send TMDS signal (what both HDMI and DVI uses). Such source port is known as DP++.

If you need to connect an HDMI source to a DP sink, you need active conversion.