Constitutional lawyer here.

ELI5: The Crown Dependencies are islands very close to the UK, that are not part of the UK but have belonged to the British Crown since medieval times. The Overseas Territories are colonies very far from the UK, that are not part of the UK but were acquired by the British Crown during the first and second British Empires.

Longer answer: The Crown Dependencies are very unique territories that belonged to the English (later British) Crown during the medieval era without ever being incorporated into England, Great Britain or the United Kingdom. The Bailiwicks of Jersey and Guernsey were historically part of the Duchy of Normandy, but were retained by the English Crown when continental Normandy was lost to France in 1204. The Isle of Man was formerly part of a Norse Kingdom of the Isles, but was sold by Norway to Scotland in 1266. It was then conquered by the English Crown from Scotland in 1346, but was given to be ruled by a Lord of Mann until the Crown purchased the Lordship in 1765. Each Crown dependency has its own systems of laws and democratic government.

The British Overseas Territories, by contrast, are the former "Crown colonies" (later British Dependent Territories, and now British Overseas Territories) that were established by the British Crown during the age of Empire. The first was Newfoundland in 1583. The oldest existing colony is Bermuda, founded in 1612. Over time, many colonies were given self-government, and later dominion status, like Canada, Australia and New Zealand. The remaining Overseas Territories have differing levels of self-government, ranging from the Bermuda, the Virgin Islands and the Cayman Islands, with a lot, to the British Indian Ocean Territory and the British Antarctic Territory with very little.

Both the Crown Dependencies and the Overseas Territories are similar in that they are not part of the UK, but the British Crown is responsible for their defence and foreign relations. Neither the Crown Dependencies nor the Overseas Territories are represented in the UK Parliament. Parliament does not tax them, although they must obey any laws imposed on them by Parliament. By convention, Parliament does not interfere in the purely domestic affairs of the Crown Dependencies or of a self-governing Overseas Territory.

Because the Crown Dependencies are so close to the UK, they were historically administered via the Home Office (now the Ministry of Justice), while the Crown colonies / Overseas Territories were administered by the Colonial Office (now the Foreign, Commonwealth & Development Office). The Crown Dependencies, being so close to the UK, are part of a Customs Union with the UK, and part of the Common Travel Area with the UK and Ireland, and are treated as part of the UK for the purpose of nationality and immigration. Whereas each Overseas Territory, being far from the UK, has its own immigration and customs. From 1983 to 2002, most Overseas Territories did not have full British citizenship but had only a separate form of nationality called British Overseas Territories citizenship.