Visa Validity is in reference to how long the Visa itself will be valid. For example, if your Visa was issued on January 1st and it is valid for 1 year, then the Visa will expire Dec. 31st.
Maximum Length of Stay is in reference to how long you can stay in the country at any particular visit. For example, China Visas allow you to stay in their country for up to 30 days. If you arrive in the country on January 1st then you must leave the country by January 30th.
Every country has its own validity requirements and length of stay rule. Some countries allow you to purchase longer validity or longer length of stay options for the visa. In some cases, you can request an extension on your visa upon arrival in the country at the Ministry of Foreign Affairs.
Note: For Non-Citizens living in the US, governments will generally only offer the least validity available.