Lymphadenopathy refers to lymph nodes pathologically increased in size. Palpable lymph nodes, on the other hand, refer to lymph nodes that you can feel, although they are normal size.
In most individuals, the only palpable lymph nodes are those around the inguinal canal. In all other cases, if you can feel the lymph nodes, they're enlarged, and there is some pathology causing them to be so.
Where it is worth remembering the distinction is in wasted patients (e.g. patients with cancer, or TB, or malnutrition). In these patients, the subcutaneous tissues are so thin that it is often possible to palpate normal (non-enlarged) lymph nodes. It would clearly be a mistake to call this lymphadenopathy.
To distinguish the two, some authorities recommend that 'lymphadenopathy' should refer only to lymph nodes greater than 1cm in diameter. Of course, this distinction is not absolute, but it is worth thinking about when feeling the lymph nodes of a wasted patient.