memcpy() vs memmove()

I'm not entirely surprised that your example exhibits no strange behaviour. Try copying str1 to str1+2 instead and see what happens then. (May not actually make a difference, depends on compiler/libraries.)

In general, memcpy is implemented in a simple (but fast) manner. Simplistically, it just loops over the data (in order), copying from one location to the other. This can result in the source being overwritten while it's being read.

Memmove does more work to ensure it handles the overlap correctly.

EDIT:

(Unfortunately, I can't find decent examples, but these will do). Contrast the memcpy and memmove implementations shown here. memcpy just loops, while memmove performs a test to determine which direction to loop in to avoid corrupting the data. These implementations are rather simple. Most high-performance implementations are more complicated (involving copying word-size blocks at a time rather than bytes).

The memory in memcpy cannot overlap or you risk undefined behaviour, while the memory in memmove can overlap.

char a[16];
char b[16];

memcpy(a,b,16);           // valid
memmove(a,b,16);          // Also valid, but slower than memcpy.
memcpy(&a[0], &a[1],10);  // Not valid since it overlaps.
memmove(&a[0], &a[1],10); // valid. 

Some implementations of memcpy might still work for overlapping inputs but you cannot count of that behaviour. While memmove must allow for overlapping.

Just because memcpy doesn't have to deal with overlapping regions, doesn't mean it doesn't deal with them correctly. The call with overlapping regions produces undefined behavior. Undefined behavior can work entirely as you expect on one platform; that doesn't mean it's correct or valid.