Disease vs Syndrome is a matter of definition
Disease
Disease is defined by underlying disorder which can present with different sings and symptoms
For example
Diabetes is a disease which has symptoms like polyuria (increased urination), polydypsia (increased thirst), polyphagia (increased hunger) and weight loss etc.
Syndrome
Syndrome is defined by set of Signs and Symptoms which present together and can be caused by one or more than one underlying disorder or the cauase may be not be clearly known
For example
Irritable bowel syndrome presents with a set of symptoms and signs including abdominal discomfort, indigestion, bloating , diarrhea alternating with constipation etc. The exact cause is not known but many have been proposed
