Main Difference
The main difference between Watt and Horsepower is that the Watt is a SI derived unit of power and Horsepower is a unit of power.

Watt
The watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, and is used to quantify the rate of energy transfer. In dimensional analysis, power is described by
M
L
2
T
−
3
{displaystyle {mathsf {M}}{mathsf {L}}^{2}{mathsf {T}}^{3}}
.

Horsepower
Horsepower (hp) is a unit of measurement of power (the rate at which work is done). There are many different standards and types of horsepower. Two common definitions being used today are the mechanical horsepower (or imperial horsepower), which is about 745.7 watts, and the metric horsepower, which is approximately 735.5 watts.
The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses. It was later expanded to include the output power of other types of piston engines, as well as turbines, electric motors and other machinery. The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With the implementation of the EU Directive 80/181/EEC on January 1, 2010, the use of horsepower in the EU is permitted only as a supplementary unit.

Watt (noun)
In the International System of Units, the derived unit of power; the power of a system in which one joule of energy is transferred per second. Symbol: W

Horsepower (noun)
A nonmetric unit of power (symbol hp) with various definitions, for different applications. The most common of them is probably the mechanical horsepower, approximately equal to 745.7 watts.

Horsepower (noun)
A metric horsepower (symbol often PS from the German abbreviation), approximately equal to 735.5 watts.

Horsepower (noun)
Strength
“political horsepower”

Watt (noun)
the SI unit of power, equivalent to one joule per second, corresponding to the rate of consumption of energy in an electric circuit where the potential difference is one volt and the current one ampere.

Horsepower (noun)
an imperial unit of power equal to 550 footpounds per second (about 750 watts).

Horsepower (noun)
the power of an engine measured in terms of horsepower
“a strong 140horsepower engine”