In the first case, you give up some of your work and nervously monitor every step of its implementation. Whereas delegation is the direction of routine functions, simple tasks, or scrupulous ones for which you do not have the proper concentration right now, to other employees.
The key is to assign the right task to the right person — who has the appropriate skills and whom you can trust, and then leave them to do it.
Do not be afraid to discuss with your superiors that some tasks are out of your competence, and it is better to reassign them. It is more useful if the task is completed on time, albeit by another person, than if you nervously study the issue instead of what you do quickly and well.