ERP and MRP difference
Introduction

Complete overview between ERP and MRP.
Historical development and evolution of Material Resource planning (MRP).


So what's the whole hassle about?
ERP stands for Enterprise Resource Planning, while MRP represents Manufacturing Resource Planning.
So there it is. That's a simple and clear explanation. You can now continue browsing more interesting topics using almighty Google.

Or...NOT?!
To really understand the difference between these two we need to go little back in history, use some analogy and - at the end - overview current business practices in order to extract "essence of the difference".

Background - in short using Wiki (simplified)
"Prior to MRP, and before computers dominated the industry, reorder point (ROP)/reorder-quantity (ROQ) type methods like EOQ (economic order quantity) had been used in manufacturing and inventory management.

MRP was created initially to supply the Polaris program then, in 1964, as a response to the Toyota Manufacturing Program, Joseph Orlicky developed material requirements planning (MRP). The first company to use MRP was Black & Decker in 1964, with Dick Alban as project leader. Orlicky's 1975 book Material Requirements Planning has the subtitle The New Way of Life in Production and Inventory Management. By 1975, MRP was implemented in 700 companies. This number had grown to about 8,000 by 1981.

In 1983, Oliver Wight developed MRP into manufacturing resource planning (MRP II). In the 1980s, Joe Orlicky's MRP evolved into Oliver Wight's manufacturing resource planning (MRP II) which brings master scheduling, rough-cut capacity planning, capacity requirements planning, S&OP in 1983 and other concepts to classical MRP. By 1989, about one-third of the software industry was MRP II software sold to American industry ($1.2 billion worth of software).
https://en.wikipedia.org/wiki/Material_requirements_planning

And what can we read about ERP...
The Gartner Group first used the abbreviation ERP in the 1990s to extend upon the capabilities of material requirements planning (MRP), and the later manufacturing resource planning (MRP II), as well as computer-integrated manufacturing. Without replacing these terms, ERP came to represent a larger whole that reflected the evolution of application integration beyond manufacturing.

Not all ERP packages developed from a manufacturing core; ERP vendors variously began assembling their packages with finance-and-accounting, maintenance, and human resource components. By the mid-1990s ERP systems addressed all core enterprise functions. Governments and non–profit organizations also began to use ERP systems.
https://en.wikipedia.org/wiki/Enterprise_resource_planning

So, as it seems, there was a good old MRP in town minding "their" own business, running as usual.
The problem was that it covered only pain in the..shoe: parts of the business where it made a sense to heavily invest in computer infrastructure. Have in mind the pricing and staff available at that time (the 80's).

As  Mr. Moore (Moore's law) decided that it is time to cut the cost of electronic components by half each year- while doubling processing power, so did the organizations decided that it is time to expand IT penetration to the different sectors in order to "boost productivity"- read Profit.
So good old MRP got himself in trouble because the new boy was in town-ERP. ERP tried to integrate all parts of the business and connect them under one roof. And then we got MODULES.

A module is a part of ERP trying to solve specific problems in corporations.
You can find MRP, HR, CRM, Project Management, Acc, MES etc.

As the internet exploded it gave birth to the first cloud-based apps.
Business apps evolved from ERP modules and you got big players, each building its career from the specially crafted cloud apps.

Todays MRP evolved from the ERP module for optimizing material resources and they incorporate Inventory management, Sales Management, Purchasing, Manufacturing.and some other features.

So basically today, from the Small Business perspective, MRP represents ERP for manufacturing companies. 

https://www.erpag.com/