"Shit" can be used as an expression of surprise, anger, or pain.
"Shit! I just slammed my finger in the car door!"
It is also used as a more familiar way of saying stuff.
"We went to the animal shelter today. They have dogs and shit."
"Let's go to Walmart. They have all kinds of shit so I'm sure will find what we need."
Something of a variation of the second meaning, it can also be used to mean "stuff that I like".
"What kind of music do you like?"
"I like Charles Mingus and Eric Dolphy."
"Ah Mingus and Dolphy, now that's my shit."
It can be used to mean poop/feces.
"The animal shelter has lot's of dog shit." (NOUN)
"My dog shits on the carpet if I don't take him outside." (VERB)
As a variation of this meaning, it can mean "bad stuff.
"Cheap toys from Walmart are always shit."
Or as an adjective, just "bad".
"Cheap toys from Walmart are always of real shitty quality."
"Bullshit" means something that's false or not completely true. It often has the implication of either the bullshit or the person saying the bullshit is taking advantage of the stupidity of others:
"Religious belief is such bullshit. No one intelligent believes in God these days."
"New-age, self-help books are all bullshit. They pretend to be profound just to make millions of dollars off of dumb, suburban housewives."
This can also be used as a verb:
"I didn't wreck your car. Maybe it was one of your friends."
"Don't bullshit me! I saw you take the car last night!"