Clarify about thread state independence.

Author: ericsnowcurrently

Doc/reference/executionmodel.rst

@@ -561,10 +561,16 @@ call stack.  It may include other thread-specific resources.
 
 Each thread state, over its lifetime, is always tied to exactly one
 interpreter and exactly one host thread.  It will only ever be used in
-that thread.  In the other direction, a host thread may have many
-Python thread states tied to it, for different interpreters or even the
-same interpreter.  However, for any given host thread, only one of the
-thread states tied to it can be used by the thread at a time.
+that thread and with that interpreter.
+
+In the other direction, a host thread may have many Python thread states
+tied to it, for different interpreters or even the same interpreter.
+However, for any given host thread, only one of the thread states
+tied to it can be used by the thread at a time.
+
+Thread states are isolated and independent from one another and don't
+share any data, except for possibly sharing an interpreter and objects
+or other resources belonging to that interpreter.
 
 Once a program is running, new Python threads can be created using the
 :mod:`threading` module (on platforms and Python implementations that