Hypothyroidism = underactive thyroid gland; treated with thyroxine tablets; may have swollen thyroid gland in neck / goitre; associated with autoimmune diseases, including Type 1 diabetes, also Turner's Syndrome and Downs Syndrome; causes body functions to slow down, leading to (some or all of the following symptoms) weight gain, tiredness / fatigue, dry skin & hair, feeling cold, constipation etc.
Hyperthyroidism (also called tyrotoxicosis) = overactive thyroid gland; autoimmune disease; most common cause is Graves disease, hyperthyroidism treated by carbimazole to reduce thyroxine production, radioactivity or surgery to remove part of thyroid gland (but may need thyroxine tablets to correct if too much is removed);
causes body function to speed up, leading to (some or all of the following symptoms): restlessness, irritability, poor sleep, loss of weight, despite increased appetite, hand tremors, heart palpitations, sweating, dislike of heat, increased thirt, needing to pass faeces more often, shortness of breath, itchy skin, thinning hair, tiredness, muscle weakness, lighter or less frequent periods (if you have them!), eye problems (with Graves disease), may cause swollen neck / goitre
(Just to confuse - goitre (swelling at front of neck) can also be caused by lack of iodine in diet eg called "Derbyshire neck" - first identified in 18th century, before improved transport links brought more fish / seafood in diet, and before iodine was added to drinking water and salt.)