These terms are found in Recursion.
1.Base Case:it is the case in recursion where the answer is 
known,or we can say the termination condition for a 
recursion to unwind back.
For example to find Factorial of num using recursion:

int Fact(int num){

if(num==1 || num==0)//base case
return 1;
else                // recursive case: 
return num*Fact(num-1);
}

2.Recursive case:It is the case whcih brings us to the 
closer answer.

Run Time Stack:It is a system stack us to save the frame 
stack of a function every recursion or every call.
This frame stack consists of the return address,local 
variables and return value if any.

Tail Recursion:The case where the function consist of 
single recursive call and it is the last statement to be 
executed.A tail Recursion can be replace by iteration.  
The above funtion consists of tail recursion case.
where as the below function does not.

void binary(int start,int end,int el){
int mid;
if(end>start){
mid=(start+end)/2;
if(el==ar[mid])
return mid;
else{
if(el>ar[mid])
binary(mid+1,end,ele);
else
binary(start,mid-11,ele);
}
}
}