Ireland runs on a parliamentary democracy. The system is set up similar to our very own government. They have a president, a house of representatives, and a senate. Though they aren't really called the house and senate, they serve just about the same purpose. The system takes longer than China's system however, because the people get a say in the actions being taken on themselves by the government.
Religion is another great difference that these countries share. Ireland has no official religion even though it is about 96% Roman Catholic. Catholicism is dominant in Ireland, mainly because of its strong English influence, but other religions aren't shunned and are welcomed to be practiced freely. China is officially atheist. Though atheist, China has a few religions that are quite abundant. Two of these are Buddhism and Taoism. Christianity is coming around in China but the government is repressing it. Christianity can only be practiced in China under strict government control. The government controls the types of Bibles, clerical appointments, and even churches. .
These countries do share much common ground though. Agriculture and industry are the main focus of these nations" economies. Over 80% of the land in Ireland is allocated to permanent pastures and croplands and potatoes are one of their largest crops. China is huge on agriculture as well. China is one of the worlds leading exporters of rice, potatoes, and many other crops. With a huge abundance of natural resources, China has also become a very industrial country. Technology is one of the greatest facets of China's industrial system. Ireland doesn't have anywhere near the natural resources of China but still holds on to a strong industrial base. .
Healthcare in China is still evolving to this day. For the longest time healthcare in China was very centralized and controlled by the government. In more recent years, the government has taken a less active roll in the healthcare in China.