Some people find it surprising that any (connected) acyclic structure can be treated as a tree, and even more surprising that any node in a given (connected) acyclic structure can be treated as the root node of a tree.
Often "hierarchical" has the connotations that there is one special privileged root node that is most important, and leaves are the least important.
When that connotation is unwanted, people often use the adjective "acyclic".
There isn't anything special or more important about any one node in an acyclic graph, because every node works fine as a root node.
A few authors use "tree" as a synonym for any connected acyclic graph.
Those authors use free tree or unrooted tree that does not yet have a root.
Later, after a root node has been arbitrarily chosen, the structure becomes a "rooted tree".
A connected acyclic graph is known as a tree, and a possibly
disconnected acyclic graph is known as a forest (i.e., a collection of
trees). -- http://mathworld.wolfram.com/AcyclicGraph.html
A tree is a set of straight line segments connected at their ends containing no closed loops (cycles). In other words, it is a simple,
undirected, connected, acyclic graph (or, equivalently, a connected
forest). A tree with n nodes has n-1 graph edges. Conversely, a
connected graph with n nodes and n-1 edges is a tree.
Trees with no particular [root] node singled out are sometimes called free trees (or unrooted tree), by way of distinguishing them from rooted trees. -- http://mathworld.wolfram.com/Tree.html
There are many practical situations that involve some some possibly-cyclic connected graph, and a variety of algorithms have been developed to cut cycles (if any) until only the minimum spanning tree remains -- a connected acyclic graph.
After a (connected) acyclic graph is built, one person can arbitrarily pick any node as the root node, and treat the rest of the acyclic structure as a tree, with all the nodes directly connected to the chosen root node as the children of that root node, then all the remaining nodes directly connected to those children as the grandchildren of that root node, and so on for every level of descendants.
A different person can arbitrarily pick some other node of that same acyclic graph as the root node, and use the same algorithm to build another rooted tree that is arranged differently than the first person's tree.