This paper has two parts: the characteristic 0 part and the characteristic p part. In the characteristic 0 part, we introduce an alternating extension of the multiple poly-Bernoulli numbers of M.-S. Kim and T. Kim. We obtain explicit representations of the alternating finite multiple zeta values, introduced by Zhao, in terms of the alternating extension of the multiple poly-Bernoulli numbers, which are alternating generalizations of the work of Imatomi, M. Kaneko, and Takeda. In the characteristic p part, we introduce positive characteristic analogs of alternating finite multiple zeta values, and express them as special values of finite Carlitz multiple polylogarithms defined by Chang and Mishiba. We introduce alternating variants of Harada's multiple poly-Bernoulli-Carlitz numbers, which are analogues of the multiple poly-Bernoulli numbers, to obtain explicit representations of the finite alternating multiple zeta values. We show that finite multiple zeta values with an integer index can be expressed as k-linear combination of FMZV's with all-positive indices.