What are the two kinds of double jeopardy?

our Bill of Rights deals with two (2) kinds of double jeopardy. 

The first sentence of clause 20, section 1, Article III of the Constitution, ordains that "no person shall be twice put in jeopardy of punishment for the same offense."

 The second sentence of said clause provides that "if an act is punishable by a law and an ordinance, conviction or acquittal under either shall constitute a bar to another prosecution for the same act."  

Thus, the first sentence prohibits double jeopardy of punishment for the same offense, whereas the second contemplates double jeopardy of punishment for the same act. Under the first sentence, one may be twice put in jeopardy of punishment of the same act provided that he is charged with different offenses, or the offense charged in one case is not included in or does not include, the crime charged in the other case. The second sentence applies, even if the offenses charged are not the same, owing to the fact that one constitutes a violation of an ordinance and the other a violation of a statute. If the two charges are based on one and the same act conviction or acquittal under either the law or the ordinance shall bar a prosecution under the other. 12 Incidentally, such conviction or acquittal is not indispensable to sustain the plea of double jeopardy of punishment for the same offense. So long as jeopardy has attached under one of the informations charging said offense, the defense may be availed of in the other case involving the same offense, even if there has been neither conviction nor acquittal in either case. 

G.R. No. L-45129 March 6, 1987
PEOPLE OF THE PHILIPPINES, petitioner,
vs.
THE HONORABLE BENJAMIN RELOVA, in his capacity as Presiding Judge of the Court of First Instance of Batangas, Second Branch, and MANUEL OPULENCIA, respondents.