Difference btw one sided test

IMO. If the null hypothesis states that the mean population is "=" to a certain value, you may use the two-tailed test. If the population mean turns out to be significantly HIGHER or LOWER, you can reject the null hypothesis (Hence the name).
On the other hand, if it uses signs other than "=" like ">" or "<", you'll only need to prove that the population mean is either higher or lower (depending on the sign used) to reject the null hypothesis. (Only one side)