There's a technical difference, politically: a realm is a territory with a monarch who is not called a king or queen. For example, Luxembourg (or The Grand Duchy Of Luxembourg) is ruled by a Grand Duke, and so is referred to as a realm rather than a kingdom. So, "realm" can be used to describe countries/territories which are "like a kingdom but don't have a king".

EDIT: Somewhat confusingly, given the above definition, "realm" can also be used to describe a kingdom, ignoring the above technical distinction. Thus a resident of the United Kingdom could talk about "The defence of the realm", meaning the kingdom.

"Realm" can also be used interchangeably with "area" when talking about knowledge - for example, you might say "This is getting into the realm of mathematics, so I'll leave it to my more technical colleagues". You'd never talk about "The kingdom of mathematics" in this way (because, again, there's no king).

There's a technical difference, politically: a realm is a territory with a monarch who is not called a king or queen. For example, Luxembourg (or The Grand Duchy Of Luxembourg) is ruled by a Grand Duke, and so is referred to as a realm rather than a kingdom. So, "realm" can be used to describe countries/territories which are "like a kingdom but don't have a king".

from https://en.wikipedia.org/wiki/Realm

EDIT: Somewhat confusingly, given the above definition, "realm" can also be used to describe a kingdom, ignoring the above technical distinction. Thus a resident of the United Kingdom could talk about "The defence of the realm", meaning the kingdom.

"Realm" can also be used interchangeably with "area" when talking about knowledge - for example, you might say "This is getting into the realm of mathematics, so I'll leave it to my more technical colleagues". You'd never talk about "The kingdom of mathematics" in this way (because, again, there's no king).

There's a technical difference, politically: a realm is a territory with a monarch who is not called a king or queen. For example, Luxembourg (or The Grand Duchy Of Luxembourg) is ruled by a Grand Duke, and so is referred to as a realm rather than a kingdom. So, "realm" can be used to describe countries/territories which are "like a kingdom but don't have a king".

"Realm" can also be used interchangeably with "area" when talking about knowledge - for example, you might say "This is getting into the realm of mathematics, so I'll leave it to my more technical colleagues". You'd never talk about "The kingdom of mathematics" in this way (because, again, there's no king).

There's a technical difference, politically: a realm is a territory with a monarch who is not called a king or queen. For example, Luxembourg (or The Grand Duchy Of Luxembourg) is ruled by a Grand Duke, and so is referred to as a realm rather than a kingdom. So, "realm" can be used to describe countries/territories which are "like a kingdom but don't have a king".

EDIT: Somewhat confusingly, given the above definition, "realm" can also be used to describe a kingdom, ignoring the above technical distinction. Thus a resident of the United Kingdom could talk about "The defence of the realm", meaning the kingdom.

"Realm" can also be used interchangeably with "area" when talking about knowledge - for example, you might say "This is getting into the realm of mathematics, so I'll leave it to my more technical colleagues". You'd never talk about "The kingdom of mathematics" in this way (because, again, there's no king).