Q:

Is there a difference between "enmesh" and "entangle"?

Is there a difference between these two words? If yes, what is it?
From Oxford English Dictionary,

enmesh

transitive. To surround with meshes; to catch or entangle in, or as in, a net. Also of the net, and fig.
fig. To entrap, entangle; to make (thought) complicated.

Enmesh seems to be very similar to entangle. What is the minor difference between them, if not subtle?

A:

From your own quoted definition:

enmesh

transitive. To surround with meshes; to catch or entangle in, or as in, a net. Also of the net, and fig.

whereas entangle means:

Cause to become twisted together with or caught in.

Therefore entangling in a net is enmeshing. But you can entangle two pieces of string together, or entangle someone in a rope; there's no mesh/net here, so it's not enmeshing.

