I understand that both are similar in structure
But how can they be easily identified as one or the other?
Is it simply based on the presence or lack of a named root (the root is identified as a particular ancestor) or outgroup?
In case of a drawn figure, either look for the a short stem to the left, or for an explicitly labelled outgroup. Trees derived from phylogenetic analyses are unrooted by default, you need to root it by either making an arbitrary (but hopefully informed) decision or by adding an outgroup.
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Trees can not be distinguished from each other because every unrooted tree can be made rooted by adding a root and vice versa by deletion.
If you mean dendrograms... the root is always the one node where the distance to each leaf is the same. But I don't know of an unrooted dendrogram.