From my perspective ,
Test suite is a collection of related test case ,
for example , Test Suite for
Check broken links in my web apps contains every test case for every links you want to check.
Test Cycle is a iteration of a Test Suite itself ,
for example you may do
Check broken links in my web apps Test Suite till it pass , so you will have several Test Cycle for that Test Suite.
And so you maybe have several Test Suites in one Test Cycle.
Source link https://sqa.stackexchange.com/questions/35044/difference-between-test-cycle-and-test-suite-in-qtest