Consider this example

Equivalence Partitioning

A pwd field should accept 8 to 15 characters. Then in case 
of Equivalence partitioning the input will be divided into 
number of classes 
 
The testcases should be 
 
-  Lessthan 8 (Should Fail) 
-  In between 8 and 15 (Inclusive of 8 and 15)  (Should 
Pass)
-  Greater than 15 (Should Fail)
 
II) Incase of B.V.A  
 
If its m to n then test cases will be m-1, m, m+1, n-1,n,n+1
 
Here it will be 7,8,9, 14,15,16 
 
6 TCs in case of BVA & 3 TCs in case of Equivalence 
partitioning. 

Equivalence class testing is a technique used to reduce the 
number of test cases to a manageable 

hope diff is clear

Equivalence partioning:-
take a example of login id field. This field can accept 
minimum 6 characters and maximum 15 characters. So in this 
technique we choose some random values like:-
a). Few values less then 6(1,3,4,5)
b). Few values between the criteria(7,9,11,13) &
c). Few values more then 15(17,21,33,45)
After making a subset of all these values,we select all the 
values one by one from the subset and enter in Login ID 
field. The value which reside in the criteria is accepted, 
rest are rejected.

Boundry value Analysis:-
We all know that Boundries are most sesitive areas and most 
error prone areas. So, all those values which are at 
boundry are tested in this technique. This is done on the 
basis of (-1,+1). 
The login ID field only accept minimum 6 characters and 
maximum 15 characters...so on the basis of (-1,+1),the 
values to be tested will be 5,6,7 for minimum and 14,15,16 
for maximum. when we implement these values one by one: 5 
and 16 will be rejected(because these values are not 
fulfilling the criteria) and 6,7,14,15 will be accepted
(these values are fulfilling the criteria)

Take an example of Textfield for Age.
Equivalence partioning:-
 It is divided into two fields:
Valid:Only Numerics
InValid:Characters and special characters.

Boundry value Analysis:-
It should accept min of 1 and max of 3
so try by entering 3+,3-,3,between 1 and 3,-1,0