What is the difference between TEXMFHOME and TEXINPUTS?

Question

A question was asked: Where do I place my own .sty or .cls files, to make them available to all my .tex files?

The accepted answer basically says the following:

1. Create a local texmf tree, say at the folder ~/localtexmf,

2. Add the folder to the search path, e.g. on a Mac running TeXLive

   tlmgr conf texmf TEXMFHOME "~/Library/texmf:~/localtexmf"
   

Another answer suggests to edit the .bashrc file and to add a line

TEXINPUTS="~/localtexmf:"

Question: What is the difference between TEXMFHOME and TEXINPUTS? Are the two solutions basically the same?