How to keep Jquery function from overwriting one input field with onclick write to second input?

Answer 1

jQuery allows you to bind multiple click event handlers. You will need to unbind the previous click event handler using .unbind before adding the second one (or both will fire, as you experienced):

$("a").unbind("click");

So your code could read:

$('.inputWithReplace').focus(function(){ 
    $("a").unbind("click").click(function(){  
     $('.inputWithReplace').val($(this).html()); 
         });  
});

Answer 2

You can shorten your code to

$(document).ready(function(){
  $('input:text').focus(function(e){ 
      tagSelector(e.target);
  });
});

function tagSelector(elem) {
  $("a").unbind('click').click(function(e){  
    $(elem).val($(e.target).text()); 
  });  
}

You might need to use a more specific selector for the inputs, I'll leave that as an exercise for you to decide :)

EDIT:

or even this

$(function(){
  $('input:text').focus(tagSelector);
});

function tagSelector(e) {
  $("a").unbind('click').click(function(){  
    $(e.target).val($(this).text()); 
  });  
}