Oracle Database Discussions

The question is...is a connection (dedicated, not shared) the same as a session? We're looking at totals derived from the follow sql stmt which I found online:

select s.username as username,
(case
      when grouping(s.machine) = 1 then
      '**** All Machines ****'
      else
       s.machine
end) AS machine,
count(*) as session_count
from v\$session s,
       v\$process p
where s.paddr   = p.addr
   and s.username is not null
group by rollup (s.username, s.machine)
 order by s.username, s.machine ;

We're seeing counts go up to about 1800+ right before the host gets into a bad state; swaps, unresponsive, etc. Can a session (dedicated) correlate one to one as a connection? We've bumped the processes param up to 5000, but now we're seeing issues with +ASM instance running into its ceiling of processes. We don't want to bump that up.

We believe the application is flawed in its ability to manage/throttle connections - we're trying to address this from the database side...are we looking at the right metrics?

Thanks in advance.