What's the difference between a telecine, a film scanner and a data-cine?

Good question! There is inevitably some cross over between these definitions but a good way of trying to determine one from the other would be to use these criteria:

Telecines - a 'video' machine, with no 'data' capability

Real Time capability(24/25/30 frames per second)
Mostly Standard Definition Video (625/525) outputs
Some have High Definition Video (e.g. 1080) outputs
Needs a Remote Control Desk (daVinci, Pandora, Tangent, ARCAS, AMIGO)
Will normally have internal Colour Correction (Primary and Secondary)
May have Internal image Manipulation (Zooms, Pans etc.)
Usually coupled with a downstream Colour Corrector (daVinci or Pandora)

Examples of Telecines; Cintel: MKIII, URSA and ADS1/2, BTS/Philips: FDL/Quadra, Sony: Vialta, Thomson: Shadow.

Scanners - a 'data' machine, with no 'video' capability

Not real time - usually somewhere around 1 frame per second
Data Resolution - 2K, 4K etc.
No 'video' output
No Colour correction or image manipulation
"Perf to perf" scan
Should have Pin Registration capability
A Cineon calibrated LOG output
Will interface direct to data storage or network
No Remote Control Desk needed but will usually require a PC Interface.

Examples of Scanners; Cintel: diTTo, dataMill and Klone, Filmlight: Northlight, Imagica: ImagerXE and HSX, Arri: Arriscan.

Data-cines - a video and data capable machine