The terms "atomic weight" and "relative atomic mass" are often used interchangeably, but they can have slightly different meanings depending on the context. Historically, atomic weight referred to the mass of an atom of an element relative to an arbitrary standard, usually oxygen, with an atomic weight of 16. This concept was widely used before the advent of modern spectroscopic techniques and the understanding of isotopes.
On the other hand, relative atomic mass is a more precise and modern term that takes into account the existence of isotopes. Isotopes are atoms of the same element that have different numbers of neutrons in their nuclei, resulting in different atomic masses. Relative atomic mass is an average mass of all the naturally occurring isotopes of an element, weighted by their abundance.
In the periodic table, you can find the relative atomic mass of an element listed below its symbol. It is usually expressed as a decimal number, and it represents the average mass of an atom of that element compared to 1/12th the mass of a carbon-12 atom.
To summarize, atomic weight is an older term that represents the mass of an atom of an element relative to an arbitrary standard, while relative atomic mass is a more precise term that takes into account the isotopic composition of the element. However, in modern usage, these terms are often used interchangeably.