Who can tell the differences between "public facility" and "public utility"?

Replying to [smelly cat]:
good question
In my opinion, public facility refer to a place while public utility refer to water supply, gas supply,etc.

Replying to [smelly cat]:
From Wikipedia, you can find the meanings for utility:

A public utility (usually just utility) is a company that maintains the infrastructure for a public service (often also providing a service using that infrastructure). Public utilities often involve natural monopolies, and as a result are often government monopolies, or if privately owned, the sectors are specially regulated by a Public Utilities Commission.

Public utilities can be privately owned or publicly owned. Publicly owned utilities include cooperative and municipal utilities. Municipal utilities may actually include territories outside of city limits or may not even serve the entire city. Cooperative utilities are owned by the customers they serve. They are usually found in rural areas. Private utilities, also called investor owned utilities, are owned by investors. Unlike private companies, private utilities may be listed on the stock exchange. Private, in this context, means not owned by the public or the government.

In poorer developing countries, public utilities are often limited to wealthier parts of major cities, as used to be the case in developed countries in the nineteenth century. However, in some developing countries utilities do provide services to a large share of the urban population, such as in the case of water and sanitation in Latin America.

Examples of utilities are:

Power
An electric utility, which in some instances can be electric power transmission or electricity distribution organizations.
Natural gas distribution
District heat generation and distribution
Water
Drinking water purification and distribution
Waste management
Sewage treatment and disposal
Other waste disposal
Transportation
Roads, including tollways
Public transport
Communication
Telephone lines
Telecomunications, such as cable television
Developments in technology have eroded some of the natural monopoly aspects of traditional public utilities. For instance, electricity generation, electricity retailing, telecommunication and postal services have become competitive in some countries and the trend towards liberalization, deregulation and privatization of public utilities is growing. However, the network infrastructure used to distribute most utility products and services has remained largely natural monopolostic.

Replying to [smelly cat]:
Again from the same source:
The word facility may refer to:

a term used to describe financial assistance programs offered by lending institutions to help companies acquire capital
an installation intended to facilitate something:
Telecommunications facility