Hi Mary,
The TIthe records were taken from about 1815 - 1842, where households were charged a tax to pay for the Church of Ireland - even Catholics had to pay this tax. Griffiths Valuation was a survey of heads of households taken from 1848 - 1864 (or so), and recorded the head of household, where they lived, how much land they had, what rent the paid etc.
Both records are often used as census substitues, they didn't cover all households, and didn't list all household members. When I haven't found all of the records for my ancestors, I've tried to create a file, listing all potential family (or people with the same surname) as sometimes you can find a father, uncle or brother listed and that helps fill out details on your tree.
This site has the full Griffiths Valuation, so you can see the actual pages. Here's all of the McAndrews that lived in Kilmoremoy on Griffiths Valuation, which was taken 1856 for Kilmoremoy.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNam…
Let me know if you want me to clarify anything.
John