Probability Density Function (PDF): This function gives the likelihood of a continuous random variable at a particular value. In the discrete cases, we call this by the name of probability mass function (PMF).
Cumulative Distribution Function (CDF): This function gives the accumulative probability of all the values less than or equal to a particular value. In other words, CDF gives accumulative probability from (negative) infinity to a said value.
Probability at a certain value is obtained by PDF or PMF depending on the case, while as probability of values less than x or probability between the range is obtained via CDF . Basic R code to understand each of these functions is explained at this link.