What are the differences between ibuprofen and acetaminophen?

Both Are Analgesics. Ibuprofen is a NSAID and can help reduce inflammation if taken at the correct dosage. Acetaminophen is an analgesic and does not offer any anti-inflammatory benefits. Both can help reduce a fever and reduce pain.
See below. http://www.diffen.com/difference/advil_vs_tylenol both medications used to relieve pain and fever, there are major differences in their mechanism of action and side effects.
Little difference. There is little or no visible difference in a child, between taking acetominophen (brand: tylenol (acetaminophen)) or Ibuprofen (brands: advil, motrin). Both are for treating fever, pain, and inflammation. Always be sure the dose is correct, and do not "double-dose" by giving other cold medicines that also contain tylenol (acetaminophen) or ibuprofen. Tylenol (acetaminophen) can be used for babies over 2 months, & Ibuprofen over 6 months old.
Time + side effects. The biggest different is that Ibuprofen lasts 6-8 hours, while Acetaminophen dosing is every 4 hours. Ibuprofen can upset an empty tummy and -- rarely -- can harm the kidneys or intestines. A large overdose of Acetaminophen can damage the liver. I personally prefer Acetaminophen for the first six months of life.
Anti-inflammatory. Both are pain relievers. However, Ibuprofen is both a pain-reliever and an anti-inflammatory. Anti-inflammatory medications help with such things as swollen joints and pulled muscles in a more effective manner than acetaminophen. Also Ibuprofen is broken-down by the kidneys and Acetaminophen is metabolized by the liver. One may need to be avoided in children with kidney or liver disease.
NSAIDs vs Tylenol (acetaminophen) Ibuprofen is a non-steroidal anti inflammatory that can be used to reduce pain and inflammation. Tylenol (acetaminophen) or Acetaminophen is a anti-pyretic medication used to reduce pain and fever, however tylenol (acetaminophen) does not reduce inflammation.
Ibuprofen. Ibuprofen stops inflammation by changing the body response, a pathway that turns on the signals to fight an inflammation. Tylenol (acetaminophen) is purely a medication that stops pain.
Both control fever. Acetaminophen is used for pain and fever, Ibuprofen is used for pain, fever and inflammation. Acetaminophen is cleared by the liver, iboprofen is cleared by the kidneys.