What's the difference between rarely and unoften?

Rarely

Definition:

(adv.) In a rare manner or degree; seldom; not often; as, things rarely seen.
(adv.) Finely; excellently; with rare skill. See 3d Rare, 2.

Example Sentences:

(1) Guillain Barré syndrome following herpes zoster is rare and only 25 cases have been reported to date.
(2) Hypothyroidism complicated by spontaneous hyperthyroidism is an interesting but rare occurrence in the spectrum of autoimmune thyroid disorders.
(3) Oculomotor paresis with cyclic spasms is a rare syndrome, usually noticeable at birth or developing during the first year of life.
(4) The frequency of rare fragile sites was studied among 240 children in special schools for subnormal intelligence (IQ 52-85).
(5) Surgical repair of the rheumatologic should however, is performed rarely, and should be reserved for the infrequent cases that do not respond to medical therapy.
(6) Cor triatriatum (CT) is a rare congenital defect, surgically correctable, and sometimes difficult to diagnose by cardiac catheterization.
(7) During this period he developed autoimmune haemolytic anaemia, a rare complication of myelofibrosis.
(8) One rare case of blind-ending branch originating in the upper third of the ureter are described.
(9) This analysis demonstrated that more than 75% of cosmids containing a rare restriction site also contained a second rare restriction site, suggesting a high degree of CpG-rich restriction site clustering.
(10) These are rare tumours comparable to abdominal desmoid tumours.
(11) They can rarely be detected spontaneously but most often are provoked.
(12) A rare case of an extradural brucellosis granuloma in the thoracic region is presented.
(13) Massive osteoplastic bone tumor in hepatocellular carcinoma is very rare.
(14) Aneurysmal bone cyst is an uncommon benign lesion that rarely presents in the craniofacial region.
(15) Axons emerge from proximal dendrites within 50 microns of the soma, and more rarely from the soma, in a tapering initial segment, commonly interrupted by one or two large swellings.
(16) Useful studies on the relationship between these acute lesions and peptic ulceration are rare.
(17) calcium tung-state, rare-earths compounds, double halogenides.
(18) Spontaneous reports of suspected adverse reactions may be the only way of revealing very rare events but they present great difficulties of rational interpretation.
(19) Metastatic tumors of the small bowel from extra-abdominal sites are rare.
(20) Perinephric abscess is a rare condition; it may be acute, but can take a chronic and atypical course as a result of incomplete treatment with antibiotics.