present tense is basically when the subject of a sentence is currently doing the verb. for example, the dog jumps over the bush. the dog (subject of the sentence) is doing the jumping right now. past tense is when the subject of a sentence already did the verb. for example, the dog jumped over the bush. the dog (subject of the sentence) has already jumped over the bush.
i think stories are more written in past tense, but i'm not quite sure. you can really do any tense you want as long as you stay consistent. i know i've written a few in past tense but currently i'm trying to switch over to present tense.