Moment.js Sandbox

HTML

<script src="//cdnjs.cloudflare.com/ajax/libs/moment.js/2.2.1/moment.min.js"></script>

JavaScript

var temp="Date between March 2018 and June 2018";
var fields=temp.split(' ');
var date2=fields[fields.length-2] +" "+fields[fields.length-1];
var date1=fields[fields.length-5] +" "+fields[fields.length-4];
const numberOfMonthsDiff = moment(date2).diff(moment(date1), 'months', true);

const dateToModify = moment(date1);

const monthsBetween  = Array.from(Array(numberOfMonthsDiff)).map(i => dateToModify.add(1,'months').format('MMMM YYYY'));

console.log(monthsBetween);