PID 22941 is the login shell from where I started the background process:

Snapshot from glance
ksh          22941  22940 241 leslie      99.8/67.6   563.8  0.0/ 0.0   268kb    1

First 2 lines from top
CPU TTY      PID 	USERNAME PRI NI   SIZE    RES STATE    TIME %WCPU  %CPU COMMAND                                                    
0      pts/t0  22941 	leslie      	    241 20   236K   256K run    	     11:41 89.57      89.41 ksh

here is ps -fu leslie from the 'other' terminal:
     UID   PID  PPID  C    STIME TTY       TIME COMMAND
     leslie 22941 22940 242 15:28:32 pts/t0   14:58 -ksh
     leslie 29326 22939  2 15:48:25 pts/t1    0:00 ps -fu leslie
     leslie 22939 22938  0 15:28:28 pts/t1    0:00 -ksh

Then I do a kill -STOP 22941 and waid a couple of minutes, followed by another ps command:
     UID   PID  PPID  C    STIME TTY       TIME COMMAND
     leslie 22941 22940  0 15:28:32 pts/t0   16:30 -ksh
     leslie  2959 22939  2 15:58:32 pts/t1    0:00 ps -fu leslie
     leslie 22939 22938  0 15:28:28 pts/t1    0:00 -ksh

Then I do a kill -CONT 22941 and just 10 seconds later ps gives:
     UID   PID  PPID  C    STIME TTY       TIME COMMAND
     leslie 22941 22940 255 15:28:32 pts/t0   16:39 -ksh
     leslie 22939 22938  0 15:28:28 pts/t1    0:00 -ksh
     leslie  3908 22939  2 16:00:40 pts/t1    0:00 ps -fu leslie