The ASVAB is developed by the U.S. Department of Defense and is administered at more than 14,000 high schools and Military Entrance Processing Stations around the United States. The Kuder Test Survey is developed by a for-profit company and administered at certified facilities --- which there are fewer of than ASVAB facilities. There is a cost to take the Kuder, depending on the company or facility. The ASVAB is free for anyone to take.
The Kuder Test Survey is intended for post-secondary students, meaning it is not meant for elementary, middle or high school students. The ASVAB, on the other hand, can be administered to military recruits at any age and since the minimum age to enlist is 18, it can be administered to students still in high school.
The Kuder focuses on three categories: skills, interests or values and career matching. The skills, interests and values, as in what is important to you in a career, that you report are used to match you with jobs. Comparably, the ASVAB tests in four areas: arithmetic reasoning, word knowledge, paragraph comprehension and mathematics' knowledge. Using the scores in each area, you are matched with a job within the military that aligns well. The ASVAB does not take into consideration your interests and values.
The ASVAB is essentially an admissions test for the military. The higher you score, the higher the rank or position that you will be offered --- with that comes a bonus, so before taking the ASVAB, test takers are encouraged to study. The Kuder measures personality traits and values which cannot be scored ordinally so there is no high score. The Kuder simply aims to match you with careers that will suit you.