In Ireland Gaelic is commonly referred to as "Irish"-- one learns Irish in school, and one may describe oneself as an Irish speaker. Marvelredneck is correct when he points out that there are numerous dialects of spoken Irish in Ireland; probably the most common would be the (much hated by Gael Linn) Dublin accented Irish spoken by the majority of school kids. I found that if one spoke Donnegal Irish it was fairly easy to understand those Gaelic speakers from the West of Scotland.

The major difference between written Irish and Scots Gaelic is the spelling, both languages having been re-cast by academics in the 19th and 20th century to make use of the modern Latin alphabet. If you really wish to read Irish or Gaelic texts in their original form (as opposed to having been translated into "modern" Irish/Gaelic) then you'll have to learn the old alphabet and its various accent marks as well.

The actual number of Irish/Gaelic speakers is a matter of much heated debate. Theoretically all children in Ireland lean Irish for the first 12 years of school. In reality, only about 12% of the population could truly be said to be Irish speakers-- the remaining 88% may have a few handy phrases in Irish, but consider English to be their primary language. In Scotland the actual number of Gaelic speakers is much lower, most estimates place it at about 3%- 5% of the population. This is not terribly surprising given that Gaelic was always a minority language, with English and Scots being the language of the vast majority of the people.