What is the difference between a desktop and workstation computer? And what brand do you think can be recommended for business and personal home use?

Workstation is a computer designed for technical or scientific applications.

Workstations are more powerful and higher in performance than desktop computers, especially with respect to CPU and Graphics, memory capacity and multitasking capability.

Can be used as a server for low level applications, I used HP Workstation xw6200 as an imaging server in the past.

Would not suggest for home or personal use due to their weight and size. Some companies still use workstations but workstation market has almost disappeared by highly commoditized hardware dominated by large PC vendors, such as Dell and HP.

For Personal or business destop machines, CMT or SFF according to your needs HP or DELL is good unless you like other brands.  For Workstatins HP is good.

Desktop would be better for your home use.

Desktop refers to a standalone computer while workstation computer is a computer which is a member or a client in a network. Two kinds of workstation computer. One is virtual desktop workstation and the other is of course the opposite of it.

For the recommendation about the brand. For me, all brands are good. I don't think that manufacturers create a substandard product. It depends on the user on how they manage their equipments.

personal computer (PC) is a general-purpose computer, whose size, capabilities, and original sale price makes it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator.
This contrasted with the batch processing or time-sharing models which allowed larger, more expensive minicomputer and mainframe systems to be used by many people, usually at the same time.
Large data processing systems require a full-time staff to operate efficiently.
Software applications for most personal computers include, but are not limited to, word processing, spreadsheets, databases, Web browsers and e-mail clients, digital media playback, games, and myriad personal productivity and special-purpose software applications.
Modern personal computers often have connections to the Internet, allowing access to the World Wide Web and a wide range of other resources.
Personal computers may be connected to a local area network (LAN), either by a cable or a wireless connection.
A personal computer may be a desktop computer or a laptop, tablet, or a handheld PC.
Early PC owners usually had to write their own programs to do anything useful with the machines, even lacking an operating system.
The very earliest microcomputers, equipped with a front panel, required hand-loading of a bootstrap program to load programs from external storage (paper tape, cassettes, or eventually diskettes).
Before very long, automatic booting from permanent read-only memory became universal.
Today's users have access to a wide range of commercial software and freeware, which is provided in ready-to-run or ready-to-compile form.
Since the early1990s, Microsoft operating systems and Intel hardware have dominated much of the personal computer market, first with MS-DOS and then with the "Wintel" (Windows + Intel) combination.
Popular alternatives to Microsoft's Windows operating systems include Apple's OS X and the free open-source Linux and BSD operating systems.
AMD provides the major alternative to Intel's central processing units.
Applications and games for PCs are typically developed and distributed independently from the hardware or OS manufacturers, whereas software for many mobile phones and other portable systems is approved and distributed through a centralized online store.[1][2] workstation is a high-end microcomputer designed for technical or scientific applications.
Intended primarily to be used by one person at a time, they are commonly connected to a local area network and run multi-user operating systems.
The term workstation has also been used to refer to a mainframe computer terminal or a PC connected to a network.
Both being microcomputers, workstations had offered higher performance than desktop computers, especially with respect to CPU and graphics, memory capacity, and multitasking capability.
They are optimized for the visualization and manipulation of different types of complex data such as3D mechanical design, engineering simulation (e.g.
computational fluid dynamics), animation and rendering of images, and mathematical plots.
Typically, consoles consist of a high resolution display, a keyboard and a mouse at a minimum, but also offer multiple displays, graphics tablets,3D mice (devices for manipulating3D objects and navigating scenes), etc.
Workstations were the first segment of the computer market to present advanced accessories and collaboration tools.
Presently, the workstation market is highly commoditized and is dominated by large PC vendors, such as Dell and HP, selling Microsoft Windows or GNU/Linux running on Intel Xeon or AMD Opteron.
Alternative Unix-based platforms are provided by Apple Inc.

Desktop is actually one of categorization in terms of Personal Computer(PC).
Examples include in this Categorization is mainly:-1.
Desktop [A simple home PC at your desk as it's wordy meaning suggests]2.
Laptop3 Tablet Now What is Work Station? A workstation is a group of computers or laptops and other network equipment such as a network printer utilizing local area network resources at one location used by a group of people.
What brands to be recommended for home and business? There are so many brands out there while for Desktop I must recommend you to buy a Dell PC for it's economical and variety in terms of it's usage.
For business I must recommend HP, IBM as high end user or MAC if plenty of graphics involved in your work environment.

The difference between both is that the Desktop is more for personal use and you can customize it as you like (add hard drives, DVD etc.).
The Workstation is for work only.
It can have limited accessibility to some programs, not customizable by you, limited hardware etc.
all depending on the purpose for its use.
The brands depend on your tastes honestly.
In a lot of companies, you will see HP, ACER.
It's quite hard to tell you which one is better because it also depends on the budget you or the company has.
For example, if you want it for gaming (desktop), "Alienware" is very recommended.
While you don't need one for work...
Hope it helped.
Regards.

workstation is Work PC Desktop is HOME PC

Desktop is normal specs pc workstation is high tech specs i.e Desktop4 GB memory, WS can take up to128 GB memory Desktop have1 CPU1 Fan, WS can have2 CPU with2 Fan Desktop power supply normal ampers (electricity), WS power supply need more Amper than desktop one