An x-ray technician is a limited permit tech. This means that there are many x-ray exams that they cannot perform. Limited techs are generally licensed to do only extremity x-rays (arms, legs, feet, hands etc) or chest x-rays, for example. I wouldn't waste my time or money on a limited tech program.
A radiologic technologist can use the title RT and has graduated from an accredited program, and can LEGALLY perform any exam involving radiation.
RTs do more than just x-rays of bones. We do fluoroscopy studies (involving the intestinal tract and barium), arthrograms (assisting the radiologist with injecting contrast or dye into joints for evaluation) and myelograms (assisting the radiologist with injecting contrast into the spinal canal). If you work in a hospital setting, you will do portable exams in ICU, CCU, the ER and even surgery. Some RTs take x-rays in the morgue. Limited permit techs cannot do most, if any, of these exams.
Most RTs will also become proficient and licensed in other modalities, such as mammography, CT and/or MRI. This training does not require any additional formal training, and is usually learned on the job. The more licenses you have, the more money you can make, as you will be in higher demand. With additional schooling, you can also do ultrasound. A limited permit tech cannot cross-train into these other modalities.
Most limited techs work in orthopedic offices. An imaging facility or hospital imaging department wants a fully licensed RT in their employ. They want a RT, who can do anything that comes through their doors. A limited tech will also make less money than a RT, if they can find a job at all.
Look at this site, and see which program is the accredited program. Just search "radiography" and your state: