In some specific usages, seeking only is often used to express hope or desire for something, while seeking only is more used to indicate that something will be pursued or obtained only under certain conditions or preconditions.
For example, "just ask for a smile" means that you just want to get someone else's smile, indicating your yearning for others' happiness and happiness. And "only seeking death" means that as long as you can die a fair death, even if it is only once, it is worth pursuing, indicating your persistence in a certain value or ideal.
Generally speaking, there is no essential difference in semantics, but the use occasions and contexts are slightly different.