Are vimrc and viminfo the same files but with different names?

They are not the same. The vimrc is the file you edit to change vim's behavior. It is a the configuration file.

The viminfo is like a cache, to store cut buffers persistently, and other things.

From the docs (:help viminfo):

The viminfo file is used to store:
- The command line history.
- The search string history.
- The input-line history.
- Contents of non-empty registers.
- Marks for several files.
- File marks, pointing to locations in files.
- Last search/substitute pattern (for 'n' and '&').
- The buffer list.
- Global variables.

In other words, Vim writes this file, not you.

Here's an example one (modified version of my own).

if has("python")
    python import sys
    python import os
    python import vim
    python sys.argv = [vim.eval("v:progname")] 
endif

set nocompatible            " Use Vim defaults (much better!)
set bs=2                    " allow backspacing over everything in insert mode
set nobackup                " Don't keep a backup file
set viminfo='20,\"90,h,%    " read/write a .viminfo file
set history=500
set statusline=%<%f%m%r%y%=%b\ 0x%B\ \ %l,%c%V\ %P
set laststatus=2            " always a status line

set dir=~/.vim/tmp//        " Put all swap files in common location (out of workspace and NFS volumes)
" set undodir=~/.vim/tmp/undo//
" set undofile
set hidden                  " allow editing in multiple buffers

set incsearch
set ignorecase
set smartcase

set scrolloff=3

" GUI options that need to be set here first
" Remove exta, useless button bar.
set guioptions-=T
set guioptions+=t

set encoding=utf-8

" Don't use Ex mode, use Q for formatting
map Q gq

" Switch syntax highlighting on, when the terminal has colors
" Also switch on highlighting the last used search pattern.
if &t_Co > 2 || has("gui_running")
  syntax enable
  set hlsearch
  " colorscheme mycolors
endif

filetype plugin on
filetype indent on

augroup cprog
  " Remove all cprog autocommands
  au!

  " When starting to edit a file:
  "   For C and C++ files set formatting of comments and set C-indenting on.
  "   For other files switch it off.
  "   Don't change the order, it's important that the line with * comes first.
  autocmd FileType *      set formatoptions=tcql nocindent comments&
  autocmd FileType c,cpp  set formatoptions=croql cindent comments=sr:/*,mb:*,el:*/,://
augroup END

augroup newfile 
  au!
  autocmd BufNewFile            *.html  0r      ~/Templates/HTML4.html
  autocmd BufNewFile            *.xhtml 0r      ~/Templates/XHTML.xhtml
  autocmd BufNewFile            *.c     0r      ~/Templates/C.c
  autocmd BufNewFile            *.py    0r      ~/Templates/Python.py
  autocmd BufNewFile            *.js    0r      ~/Templates/Javascript.js
  autocmd BufNewFile            *.txt   0r      ~/Templates/RST.rst
  autocmd BufNewFile            *.rst   0r      ~/Templates/RST.rst
augroup END

If .vimrc does not exist, you should create it. I recommend to host the configuration file in github, and create a symbolic link to your .vimrc