They both deal with attraction. Asexual means no sexual attraction and aromantic means no romantic attraction.
A relationship doesn't necessarily need both or either of that. Like, you can be in a relationship even if you're aro, ace or both. That also heavily depends on the people involved and what they imagine a relationship to be.
Also, both aromanticism and asexuality are spectrums so depending on where the person is, there'll be differences.
There are some nice definitions and stuff on this site for aromanticism:
And if you want to know more about asexuality, I'd recommend having a look at this site:
https://www.asexuality.org/