There are some countries that allow youngsters of age 16 to enter a club/bar. Some countries need to be 18. A few clubs that I know needs the person to be of the age 21 in order to enter that establishment. Why is it that there are age limits on different countries? Is it because teenagers in certain countries mature differently from other countries?

It depends on the culture of the country, and what is considered the norm for certain age-groups. Some countries let you drink alcohol or drive a car at about 14 for instance. The area you grow up in and what is common-place there has an effect on your maturity.