个人理解，如有不正确的地方望斧正。

顾名思义，mutable：可变的。如：NSMutableArray，可变数组；NSMutableDictionary，可变字典；NSMutableString，可变字符串等等。

mutableCopy，就是copy一个mutable的对象，如上。也就是所谓的深拷贝。
copy，就是copy一个NSArray,NSDictionary,NSString等等这类的对象。就是所谓的浅拷贝。

网上查阅资料发现，浅拷贝，copy的是指针，并没有copy里面的内容。深拷贝，就是把里面的内容也给拷贝了。

基于以上理解，我写了如下Demo:

NSString *string1 = @"YES";
NSString *string2 = [string1 copy];
NSLog(@"string1 is %@",string1);
NSLog(@"string2 is %@",string2);
string1 = @"NO";
NSLog(@"string1 is %@",string1);
NSLog(@"string2 is %@",string2);

因为拷贝的只是指针，所以当指针指向地址的内容发生变化时，string1和string2都会发生变化。Run it

string1 is YES 
string2 is YES 
string1 is NO
string2 is YES 

脸疼。Why？进一步详细输出日志

NSString *string1 = @"YES";
NSString *string2 = [string1 copy];
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);
string1 = @"No";
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);

Run

string1 is YES address is 0x10f6d41a0
string2 is YES address is 0x10f6d41a0
string1 is No address is 0x10f6d4200
string2 is YES address is 0x10f6d41a0

可以看到string1的指针地址确实复制给string2了，但之所以string2没有跟着string1变化而变化，是因为在string1 = @"No";时，string1指向了其他的地址，而string2还在之前的地址。所以string1变成了新的，而string2不变。
因为NSString对象是不可变的，你不能直接改变他的内容，只能重新给他赋值，而赋值，就会指向新的地址。
如果我们采用NSMutableString

NSMutableString *string1 = [[NSMutableString alloc]initWithString:@"YES"];
NSString *string2 = [string1 copy];
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);
[string1 appendString:@" or Not"];
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);

string1 is YES address is 0x608000267400
string2 is YES address is 0xa000000005345593
string1 is YES or Not address is 0x608000267400
string2 is YES address is 0xa000000005345593

copy只能复制不可变的对象，所以对可变的NSMutableString进行copy时，已经生成了新的对象。
做到这儿了再来试试mutableCopy

NSMutableString *string1 = [[NSMutableString alloc]initWithString:@"YES"];
NSMutableString *string2 = [string1 mutableCopy];
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);
[string1 appendString:@" or Not"];
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);

string1 is YES address is 0x618000072240
string2 is YES address is 0x618000072140
string1 is YES or Not address is 0x618000072240
string2 is YES address is 0x618000072140

由此推论，所谓的深拷贝，只拷贝了内容，并没有拷贝指针。
如果我们想要既拷贝内容，又拷贝指针咋办？什么都一样其实就是同一个对象了。

NSMutableString *string1 = [[NSMutableString alloc]initWithString:@"YES"];
NSMutableString *string2 = string1;
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);
[string1 appendString:@" or Not"];
NSLog(@"string1 is %@ address is %p",string1, string1);
NSLog(@"string2 is %@ address is %p",string2, string2);

string1 is YES address is 0x61800006d5c0
string2 is YES address is 0x61800006d5c0
string1 is YES or Not address is 0x61800006d5c0
string2 is YES or Not address is 0x61800006d5c0

综上，
1、copy针对不可变对象，只拷贝指针。（但因为不可变，所以内容也就一样不会变。）如NSString，string2 = [string1 copy];等效于string2 = string1。
2、mutableCopy针对可变对象，只拷贝内容，会分配新的指针地址。所以如NSMutableString，string2 = [string1 mutableCopy];就不等效于string2 = string1。
3、可变对象进行copy的话，指针地址会发生改变。不可变对象进行mutableCopy的话，指针地址也会发生改变。

以上是对copy与mutableCopy的理解，顺便提一下，不是所以的对象都可以copy与mutableCopy的，用户自定义的NSObject需要实现NSCopying 协议，然后自己实现copyWithZone或者mutableCopyWithZone方法。
(关于property中的copy在这一篇)

最后警醒一下自己：

NSString *string = @"test";
NSString *copy1 = [string copy];
NSString *copy2 = [string mutableCopy];
NSMutableString *copy3 = [string copy];
NSMutableString *copy4 = [string mutableCopy];
NSLog(@"string is %@ address is %p &address %p",string, string, &string);
NSLog(@" copy1 is %@ address is %p &address %p",copy1, copy1, &copy1);
NSLog(@" copy2 is %@ address is %p &address %p",copy2, copy2, &copy2);
NSLog(@" copy3 is %@ address is %p &address %p",copy3, copy3, &copy3);
NSLog(@" copy4 is %@ address is %p &address %p",copy4, copy4, &copy4);

string is test address is 0x1092191a0 &address 0x7fff56a22a38
 copy1 is test address is 0x1092191a0 &address 0x7fff56a22a30
 copy2 is test address is 0x60000026ea00 &address 0x7fff56a22a28
 copy3 is test address is 0x1092191a0 &address 0x7fff56a22a20
 copy4 is test address is 0x60000026efc0 &address 0x7fff56a22a18

之前陷入误区，&string去取指针地址，发现每一次的地址都不相同。其实我们的string本身就是指针变量，%p即是指针地址，如果再加上&，取的是指针的指针的地址。
同志仍需努力啊！