Ibid is an abbreviation of ibidem, a Latin word that means, literally, in the same place. Ibid is used mainly in footnotes or references to note a source that was previously mentioned, saving time and space by not repeating the same thing over and over again. Note here that it is the exact same source in the exact same place, so the duplicate citation would be exactly the same.
Some style guides and dictionaries will tell you to use a period with ibid., others will say it is fine without, some will tell you to italicize it because it is Latin, and yet others will say it can be further abbreviated to ib.
Since it is used in footnotes, reference the style guide for your publication and follow the direction given there.
Idem is also Latin, literally meaning the same. It is abbreviated id. and used primarily to denote a source previously cited. This is used often in bibliographies.
Id can be the same source, but usually a different page or section. It is not an exact replica like ibid.
The same period, italicization, and capitalization issues plague id and style guides should be referenced.
However, the rules exempt indigents from payment of the said filing fees as long as their petition is supported by a certification from the city or municipal social welfare office that the petitioner is an indigent (Rule 10, Ibid.). [The Manila Times]
The investigation involved allegations that between 2007 and 2011 Goodyear’s subsidiaries in Kenya and Angola paid more than $3.2 million in bribes to “employees of government-owned entities and private companies to obtain tire sales.” Id. at 2. [JD Supra]