This question is often asked and discussed even by specialists in embedded systems . There is, as with many, a spectrum, and simple definitions are complex.
My preferred definition: a system containing one or more computing or processing elements that are not a general purpose computer.
Some systems are undoubtedly built into this definition and include elements such as washing machine controllers, telephone switches, satellite navigation equipment, marine chart plotters, car ECUs, laser printers, etc.
Some of them are not so easy to classify. The first-generation digital mobile phone is probably an embedded system, while more modern features and smartphones, however, are somewhat different. They can run applications selected and installed by end users, which allows them to perform tasks not specified by the manufacturer. With growing capabilities, they are essentially portable computers and a set of applications sufficient to be considered "universal."
With these more controversial systems, it is useful to ask, perhaps, not what is an embedded system, but what is the development of embedded systems? For example, the manufacturer of your smartphone deployed the operating system on it, the signal processing and communication stack necessary to operate as a phone, all device drivers and stacks for WiFi, USB, data storage, etc., and this, of course, is development embedded systems. However, guys writing applications for PlayStore or AppStore, etc., write on a specific common platform, abstracted from all this embedded code - this is not the development of embedded systems by any definition that I would accept if, perhaps, the application was not intended for some bespoke vertical market app. - like, for example, applications for signing delivery, which the UPS drivers on the PDA have, in this environment the "universal" device was renamed to the "special" device.
In relation to the PC; A PC may be an embedded computing element in a system that is not a general purpose computer. Industrial PCs are usually integrated in manufacturing and packaging equipment, CNC machines, medical equipment, etc. Although they share a common hardware architecture with desktop PCs, they do not necessarily look like desktop PCs and have many different form factors for both boards and chassis. However, even on a desktop PC there are many examples of embedded computing elements and embedded software, such as the BIOS, which is responsible for loading the system, such as the keyboard controller and the drive controller.