Dozing in the sun at the beach after swimming, limbs exhausted, salt dring stiff in my hair.
Cutting up vegetables into neat pieces.
Flying into a city and at night seeing the lit gauze of its streets from the air.
Cycling on a balmy night when the streets are quiet.
Taking a bath when I’m a little drunk.
Stretching out my muscles, sitting in the floor.
All of the examples quoted are phrases. They are not complete sentences. It would be better if examples in complete sentences are provided to distinguish the differences.
In short, according to my understanding, a gerund functions more like a noun (e.g. as subject, object, etc.). For example, I love cycling on a balmy night when the streets are quiet.
A (present) participle can take up the function of a verb, or an adjective. If a participle takes up the function of a verb, it is common for it come with a subject in the complete sentence. For example, Stretching out my muscles, sitting in the floor, I feel so relaxed.