Define: Lux versus Lumens

Last time, I learnt about Fenstration. Lighting terms I learn from my consultation with lighting consultants:

 According to wikipedia -
The difference between the units lumen and lux is that the lux takes into account the area over which the luminous flux is spread. A flux of 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an illuminance of 1000 lux. 

This leaves me still unsure as we always ask to know the lighting specs before purchasing the metal halides or the LED lighting for TPM's various static displays. We also get specs with lux quoted based on our digital LCD digital Out of Home displays. So what is lux and lumens scientifically.

Via the above YouTube video, I even got to know about the term candela. This candela is not as applicable to Out-of-Home lighting. But overall, this video is very straight forward explanation indeed.