TL;DR: A function can be reentrant, thread-safe, both or neither.
The Wikipedia articles for thread-safety and reentrancy are well worth reading. Here are a few citations:
A function is thread-safe if:
it only manipulates shared data structures in
a manner that guarantees safe execution by multiple
threads at the same time.
A function is reentrant if:
it can be interrupted at any point during its execution
and then safely called again (“re-entered”) before its
previous invocations complete execution.
As examples of possible reentrance, the Wikipedia gives the example of a function designed to be called by system interrupts: suppose it is already running when another interrupt happens. But don’t think you’re safe just because you don’t code with system interrupts: you can have reentrance problems in a single-threaded program if you use callbacks or recursive functions.
The key for avoiding confusion is that reentrant refers to
only one thread executing. It is a concept from the time when
no multitasking operating systems existed.
Examples
(Slightly modified from the Wikipedia articles)
Example 1: not thread-safe, not reentrant
/* As this function uses a non-const global variable without
any precaution, it is neither reentrant nor thread-safe. */
int t;
void swap(int *x, int *y)
{
t = *x;
*x = *y;
*y = t;
}
Example 2: thread-safe, not reentrant
/* We use a thread local variable: the function is now
thread-safe but still not reentrant (within the
same thread). */
__thread int t;
void swap(int *x, int *y)
{
t = *x;
*x = *y;
*y = t;
}
Example 3: not thread-safe, reentrant
/* We save the global state in a local variable and we restore
it at the end of the function. The function is now reentrant
but it is not thread safe. */
int t;
void swap(int *x, int *y)
{
int s;
s = t;
t = *x;
*x = *y;
*y = t;
t = s;
}
Example 4: thread-safe, reentrant
/* We use a local variable: the function is now
thread-safe and reentrant, we have ascended to
higher plane of existence. */
void swap(int *x, int *y)
{
int t;
t = *x;
*x = *y;
*y = t;
}