[Sweet]

truten, например, так:

var string = 'Lorem <div>ipsum dolor</div> sit amet, consectetur <div>adipisicing elit</div>, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, <div>quis nostrud exercitation ullamco</div> laboris nisi ut aliquip ex ea commodo consequat.';
alert(getInnerStrings(string, "div"));

function getInnerStrings(string, tagName) {
  var openTag = "<" + tagName + ">";
  var closeTag = "</" + tagName + ">";
  
  var substrings = [];
  
  for (var position = string.indexOf(openTag); position != -1; position = string.indexOf(openTag, position)) {
    position += openTag.length;
    
    var closeTagPosition = string.indexOf(closeTag, position);
    if (closeTagPosition == -1) throw new Error("parse error");
    
    substrings.push( string.substring(position, closeTagPosition) );
    position = closeTagPosition + closeTag.length;
  }
  
  return substrings;
}