What is the difference between shape file and feature class?

• The difference is : in save type only ; thats mean if I save shape file in GDB it's called feature class and if I save shape file without GDB it's called shape file 
• To make shape file you have to make folder on any local disk after that go to  : ArcCatalog/ folder connection/chose your folder which u want to save shape file within/right click on the folder/new/shafe file.../put the name &type(point,polyline or polygon)/ok
• To use it :ArcMap /add it(shape file which u make it) from add icon /edittors/start editing/Do what u want to do/editors/save erit/stop editing.

Both shapefile as well as feature class are different way to store vector geospatial data in the storage medium (Server or PC hard disk).

Shapefile is designed by ESRI (Environmental System Research Institute. It is a light weight vector data storage mechanism based on split technology also known as georelational data model. This file system consists of three mandatory files *.shp (it store the shape or geometry) and *.dbf (it stores tabular information related the shape represented in the *.shp file) and *.shx (a file that stores the index values to connect the split files – SHP and DBF). For example, if a road data is sorted in SHP file; its name, width, speed limit (non spatial information) are stored in DBF file and these two files are connected by means of SHX file. Apart from these three mandatory files there are other optional files related to a shapefile. This is the simplest method of represent features which lack high precision/accuracy.  

For more info read:  http://www.esri.com/library/whitepapers/pdfs/shapefile.pdf

Feature class is the fundamental unit of a geodatabase. It is based on object data model. Apart from shapefile, feature class can have topology (to make data more precise/accurate)-Eg. your country boundary may have100Sq.Km area and another feature class contain individual counties/states together will also have same area as country boundary (this may not be achieved in shapefile, in shapefile the area may be >100Sq.KM or <100 Sa.Km ( due to overlap or gaps between features in the county/states shapefile). There is only one file is used for the geodatabase that is *.msd (Microsoft Jet data engine). All the shapes and non spatial information are stored in a single file.

For more info read:  http://resources.arcgis.com/en/help/main/10.1/index.html#//003n

To create a feature class, open ArcCatalog/ArcCatalog window (10x and above), decide the location to store your feature class. Right click 'Content' Tab, and goto New, and click File Geodatabase or Personal Geodatabse- provide a name. Click open the geodatabse and again right click and goto New again and specify feature class-now the window is a wizard and you can provide details such as - give a name- if need, give a alias name, select type-point, polyline or polygon...select appropreate projection, click next and specify field name and data type if required. click finish to complete the procedure.

shape file is an old format for GIS data developed for Arcview software. while Feature class is the new format for creating layers of GIS data in what is called now geodatabase.

By this definition, a Shapefile is a Feature Class. Back in the 1990’s, the Shapefile was referred to by it’s full name – the Shapefile Feature Class. Think of “Shapefile” as it’s Given Name, and Feature Class as the Surname. If we always referred to it’s full name, Shapefile Feature Class, the comparison (or lack of) would not need to be discussed. This also helps explain a Geodatabase Feature Class. The Given name for both, really describes the Workspace type. Hopefully a Workspace in ArcGIS python or ModelBuilder makes more sense now too.

This brings up another discussion on the Shapefile vs Feature Class topic. What is there to compare with a Shapefile Feature Class and a Geodatabase Feature Class? There are many similarities, since they are both collections of common features having the same spatial representation (Point, Line, Polygon, etc). The differences are mostly in the additional types and behaviours available to a Geodatabase FC. Not going to list them all, but domains, topologic relationships (geometric networks, terrains), and the ability to store high precision geometry are a few differences. And there are many Geodatabase storage options: Access (AKA Personal), File, and Enterprise (AKA RDBMS) which can have subtle differences as well. Whereas a Shapefile is always stored in a file folder and is more of a universal format support by many

The difference is : in save type only ; thats mean if I save shape file in GDB it's called feature class and if I save shape file without GDB it's called shape file 

[ESRI software] In  ArcGIS, a collection of geographic features with the same geometry type  (such as point, line, or polygon), the same attributes, and the same  spatial reference. Feature classes can be stored in geodatabases,  shapefiles, coverages, or other data formats. Feature classes allow  homogeneous features to be grouped into a single unit for data storage  purposes. For example, highways, primary roads, and secondary roads can  be grouped into a line feature class named "roads." In a geodatabase,  feature classes can also store annotation and dimensions. 

Shape file may or may not contains projection system while feature class MUST have coordination system

the same attributes, and the same spatial reference. Feature classes can be stored in geodatabases, shapefiles, coverages, or other data formats.

Shape file and feature class are the same as they serve the same purpose but the difference is that shapefiles are stored in file folder while feature class are mainly used in geodatabase.