What is the difference between the sign of the end of a verse and the letter "ق" (Qaf) in the Holy Quran, knowing that both necessitate a pause?

Stopping at the end of verses is a Sunnah (definition), and it is not obligatory by the consensus of reciters. As for stopping at the signs in the Mushaf (definition), such as (قلي - Qali), (صلي - Sali), and (م - Mim), this is a matter of ijtihad (definition) (independent reasoning) and convention, and it does not necessitate stopping, except for the sign (م - Mim), which indicates an obligatory stop. This is because continuing the recitation would suggest an unintended meaning. An example of this is stopping after "فلا يحزنك قولهم" (so let not their speech grieve you), because continuing would suggest that "إنا نعلم ما يسرون وما يعلنون" (Indeed, We know what they conceal and what they declare) is part of the disbelievers' speech. Similarly, stopping after "إنما يستجيب الذين يسمعون" (Only those who listen will respond) is necessary so that continuing does not imply that the dead share with the living in responding.