The linked definitions are slightly misleading if the actual context is not clarified. SIPp can be used to measure the QOS quality of service of a SIP system and the QOS need to be evaluated using traffic data.
In practice, you would normally measure the actual traffic and use that figure to work out how many lines you need in a specific instance.
If you are tacking with more instances (read a solution deployed in various different cases) then a kind of traffic modeling is necessary with the concept of CPS "How many calls per seconds do the system is able to take in?"
So far so good but imagine for example, if a group of user made 100 calls in one hour.
On one hand, each user is making the call randomly then the actual distribution of calls is smooth during the hour (Poisson law in math)
on the other hand, if users are not making calls randomly but all at the same time then 100 calls will be received at once.
CAPS is able to represent the peak "how many calls attempts at peak do the system is able to take in?"
In summary, CPS is giving us a measure of the carried traffic on the system and CAPS is more a measure of the offered traffic load.
Btw, CPS is not useless but rather inappropriate in certain cases.
If you want to go further, erlang modelling and queuing theory are the math backing traffic modeling.
