using vi

entering four consecutive space characters with the tab key

Add set tabstop=8 softtabstop=0 expandtab shiftwidth=4 smarttab to $HOME/.exrc.

Explanation (incomplete)

tabstop is the width of a hard tabstop measured in "spaces". It is effectively the (maximum) width of an actual tab character.
softtabstop. Setting this to a non-zero value other than tabstop will make the tab key (in insert mode) insert a combination of spaces (and possibly tabs) to simulate tab stops at this width.
expandtab. Enabling this will make the tab key (in insert mode) insert spaces instead of tab characters. This also affects the behavior of the retab command.
shiftwidth. The size of an "indent". It's also measured in spaces, so if your code base indents with tab characters then you want shiftwidth to equal the number of tab characters times tabstop. This is also used by things like the =, > and < commands.
smarttab. Enabling this will make the tab key (in insert mode) insert spaces or tabs to go to the next indent of the next tabstop when the cursor is at the beginning of a line (i.e. the only preceding characters are whitespace).
.exrc is the startup file for vi.¹

Some rights reserved: CC BY-SA 3.0. Includes significant content from an answer on Stack Overflow by Laurence Gonsalves, with changes made.