Hi Niwatha,
An uneducated person may not be ignorant, vice versa. An uneducated person does not have formal schooling and may have low levels of literacy and numeracy. In contrast, an ignorant person is not aware of the incompleteness of their knowledge though they may be educated.
An educated person may know a lot of theoretical knowledge but may ignorantly form conclusions based on their limited understanding. An uneducated person may not know how to read and write, but is keenly aware of his intellectual deficiency. Such an awareness shows that the uneducated person is not ignorant.
If someone appears not to know something that they should, we consider them ignorant (e.g. a teacher who does not know how to write a lesson plan). If someone does not show consideration to others, we consider them ignorant too. In this case, we may be educated yet ignorant.
Is it possible for someone to be ignorant and uneducated? Well, it is. For example, some of us have little knowledge on financial planning because schools tend not to teach such important life skills. As a result, some of us grow up uneducated in this area and do not bother to plan well for retirement due to our ignorance.
Failure to be educated may lead to ignorance; ignorance may lead someone to neglect education. Some people may be ignorant, uneducated or both; however, the meaning "ignorant" and "uneducated" are not the same.
This discussion reminds me of something that my university professor shared: The more I know, the more I should know that I don't know. (It means that the more educated I am, the less ignorant I should be because I become more aware of the infinite nature of knowledge.)
I hope this helps.