Hi Ryan,
Both words have their similarities as well as subtle differences. For a start, both words describe pleasant smells, with "fragrance" defining a sweet pleasant smell. "Fragrance" is the pleasant scent of something, but "aroma" is something that encompasses more than a pleasant smell. Something that is aromatic gives off a distinct pleasant odour and can also tantalise our taste buds.
As an example, when we stand beside a batch of roasted coffee beans, we know the smell is emanating from coffee beans as we recognise its fragrance. After ordering a cuppa, we sit down and allow the smell to waft into our nostrils before taking a sip. The taste of the coffee could be acidic, smoky, fruity or floral. The smell and the delicious taste of the coffee makes up its aroma.
That is why we hear people commenting on the "fragrance" of a cologne or rose but others enjoy the aroma of coffee or tea.