I understand there is a difference between the two. But how can I tell?
A full node is a node that validates all network rules, regardless of whether it listens for incoming connections or not. Bitcoin Core is full node software which always does this.
To see whether you can be reached by others, look at the network view and see if you have any incoming connections. Note that it may takes hours to days before your IP address is sufficiently well known to others on the network to make connections to you.