Question: What is the difference between radiation doses of a medical scanner and airport security scanner (X-Ray full body scan)? Is it the same kind of radiation? Does it pose any danger for people who fly often?

Answer: 
The type of radiation is quite different in a medical X-ray vs. an airport scanner. 

Medical X-rays are high frequency (beyond ultraviolet) radiation, typically on a wavelength of a few angstroms. While I would emphasize that @Ram is right to point out that there [is not very much radiation](http://hps.org/physicians/documents/Doses_from_Medical_X-Ray_Procedures.pdf) in a medical X-ray since electronic detectors have been in place over film, the radiation itself is capable of penetrating the entire body and causes ionization. The body can tolerate a certain amount of this, but that's why we use X-rays - they go through just about anything but bone/minerals and metals. 

Airport security scanners emit [terahertz radiation](http://en.wikipedia.org/wiki/Terahertz_radiation), which has a wavelength between microwave and infrared. This is a very low level of energy per photon. Terahertz radiation will not penetrate more than a centimeter of light material, which is more suitable to find hidden metal objects (which reflect terawaves). Relative to X-rays it causes practically no radiation damage. The intensity of the radiation is also pretty low since these scans are also detected by digital cameras, which are quite sensitive. 

Compare the machinery. X-ray technicians, who might have to take dozens of X-ray exposures a day, usually go behind a protective screen to take a medical x-ray. The airport body scanners are open to the air and the terahertz radiation spills out into the crowd and the workers stand by it every day. It has practically no expectation of being hazardous. This device is pretty good as frequent fliers can have as many scans per year as are needed and health concerns are not significant. 

Its always possible we might find some issues with Terahertz radiation in the future, but its hard to imagine it - its safer than standing 2 feet away from a working, closed oven.
As per the American Association of Physicists in Medicine the radiation exposure from full body airport scanners is equivalent to what an individual receives every 1.8 minutes on the ground from natural background radiation or equivalent to every 12 seconds during an airplane flight. 

<http://www.aapm.org/pubs/reports/RPT_217.pdf>

The Back scatter full body scanners at airports use X-rays.