S isn't stopped. it's "interruptable sleep". Only 1 process can technically be running at a time on each CPU. T is the code you want to look out for. That means stopped by job control. see man ps for the state codes. Here's the relevant section from GNU/Linux:
PROCESS STATE CODES
Here are the different values that the s, stat and state output specifiers (header "STAT" or "S") will display to describe the state of a process:
D uninterruptible sleep (usually IO)
R running or runnable (on run queue)
S interruptible sleep (waiting for an event to complete)
T stopped, either by a job control signal or because it is being traced
W paging (not valid since the 2.6.xx kernel)
X dead (should never be seen)
Z defunct ("zombie") process, terminated but not reaped by its parent
For BSD formats and when the stat keyword is used, additional characters may be displayed:
< high-priority (not nice to other users)
N low-priority (nice to other users)
L has pages locked into memory (for real-time and custom IO)
s is a session leader
l is multi-threaded (using CLONE_THREAD, like NPTL pthreads do)
+ is in the foreground process group