What is the difference between MOSFET transistor and normal transistor?
[From Question]: MOSFET transistor and normal transistor


A MOSFET is a normal transistor - it's a Metal-Oxide-Semiconductor Field-Effect Transistor

A BJT is another normal transistor - a Bipolar Junction Transistor

The question itself doesn't make much sense in that regard. But lets assume for now you mean BJT when you say "normal".


  [From Question]: but there shapes is different


Are they? Transistors come in packages of many shapes and sizes


  [From Comment]: left one is "normal", and right is MOSFET


The picture shows two different packages, however this is no indication of type.

Equally the left one could be a MOSFET (e.g. BS170 comes in a TO92 package). The right one could be a BJT (e.g. TIP41 comes in TO220 package).


  [From Comment]: pictures for the symbols 


This is where things start to differ. 

In your picture, the symbols are misleadingly labelled. 


The top symbol, labelled "transistor" is the symbol for a BJT. This is indeed a "transistor".
The bottom symbol is indeed a MOSFET. However this is also a "transistor".


There are also more than two types - e.g. JFET (Junction FET), MESFET (Metal-Semiconductor FET).



The reason for the difference in symbol and behaviour between a BJT and MOSFET is due to the way that the two types of transistor work differently, and exhibit different behaviour. 

In simplest terms, we can say:


A BJT transistor is a current controlled device. That is to say the current flowing into the base of the transistor controls the current flowing into the collector.
A MOSFET is a voltage controlled device. The voltage you apply across the gate controls how much current flows into the drain.


In other words their behaviour is different. Both are transistors, but are used in different ways. I won't go into any more details in this answer, there are plenty of resources into the behaviour of MOSFETs vs BJTs.