Can I submit the results of a poster to another conference as a full paper? If I presented a poster at a conference that contained the results of some research, can I then write a paper using those same results and submit it to another conference as a full paper?
This depends on the customs of the field and the venue. I will answer based upon my experience from an HCI-related subfield of CS:

Conferences usually have some requirement of novelty for published works. Therefore, if a paper associated with the poster already appeared in some proceedings of the first conference, you might not fulfil this requirement. First, however, some different cases might apply:


If the poster was not "formally published" (i.e. did not appear as a (short) paper in any kind of proceedings), you should be good to go.
If the poster was supposed to be "formally published", but the conference organizers never got around to setting up the proceedings of the poster session, you're in a bit of an inconvenient situation. Your work is not published in a way that it can be cited (well, it can, but it doesn't look as verifiable as other papers and is not archived by any publisher), but it has been presented. You may want to contact the conference organizers in this case whether publishing your work again is ok, or else you may want to wrap your work in something larger (i.e. present something new, but reiterate the points from the poster as a part of the exposition).


Even if your poster was published in some kind of proceedings, there may be some options:


Posters are often allowed to present work in progress. If your poster (and the connected paper) was presented in a way to present work in progress, your new conference paper might indeed present the final state of whatever you devised. This can essentially match the content of your poster, but provide more details (see also below).
Even if the poster presented final results, the term "results" seems to be seen in a very wide sense at least in my fields, possibly in others. A full conference paper provides much more space than a poster paper, and on the poster, you probably presented different (more visual) things than you would in text. As such, you can shift the focus of your conference paper compared to the poster; where the poster focused on the results, the conference paper might discuss the methods used to obtain the results in depth, including design decisions, citations of similar experiments, a verification of the reliability of your experiments, etc. This kind of description can be useful for the community and subsequent works, and as such should provide enough new content, despite being based upon the same material as the poster.