Translation:Please help me buy some things.
The differences I know are that 帮 is a verb referring to "helping" or "doing something for" someone, 帮助 can be both a verb and a noun meaning "help" but is not really used for asking people to "do something" for you and more for "asking for help". Sorry if this wasn't that clear but I hope it helps
Please help me buy "SOME STUFFS". (I'm not suggesting this as translation, but rather as a gloss of what is going on in the Chinese-speaking brain when saying this.) I had a Chinese girlfriend who always said "some stuffS" and I think she was translating dongxi without realizing "stuff" cannot be made plural.
In a previous sentence, "Wo de ma ma xiang mai yi xie dong xi," I remarked that it looked funny. Here, I think "yi xie" is ok. The person is trying to tell the friend that he is asking for a small favor- "Please help me buy SOME things." If he then gave me a 30 page list, I would be pissed.