Vertical alignment instructions are reversed with tabular

I'm not sure what you mean when you say that the columns influence each other. The output is precisely what it should be. The p-column is basically a top-aligned parbox, the b-column a bottom-aligned one, and the m column a center-aligned one. If I add the baselines in your tabular

documentclass{article}
usepackage[utf8]{inputenc}
usepackage{array}
setlength{arrayrulewidth}{1mm}
setlength{tabcolsep}{18pt}
renewcommand{arraystretch}{1.5}

deffoo{leavevmodehbox to 0pt{hss vrule width 5cm height .4pthss}}


begin{document}
begin{tabular}{|m{3cm}|b{3cm}|p{3cm}|}
  hline
  multicolumn{3}{|c|}{Country List} 
  hline
  foo Country Name or Area Name& ISO ALPHA 2 Codefoo & foo ISO ALPHA 3 
  hline
  Afghanistan & AF &AFG 
  Aland Islands & AX   & ALA 
  Albania &AL & ALB 
  Algeria    &DZ & DZA 
  American Samoa & AS & ASM 
  Andorra & AD & AND   
  Angola & AO & AGO 
  hline
end{tabular}
end{document}

you'll see that the bottom line of the second (b) column is correctly aligned with the top (and only) line of the third (p) column; the first column (m) is centered, so its top baseline is higher.

To make more clear what the alignment with respect to the baseline means, consider the following sequence of three parboxes

documentclass{article}
newcommand*{baseline}{rule{1cm}{.2pt}}
newcommand*{foo}[1]{{setlength{fboxsep}{-fboxrule}fbox{parbox[#1]{1cm}{raggedright Foo bar baz bar}}}}
begin{document}
baselinefoo{c}baselinefoo{b}baselinefoo{t}
end{document}