24 hour visa free transit

You have clearly stated that your transit time will be shorter than 24 hours. If this is the case, your transit will be covered by 24 hour visa free transit and you do not need any kind of visa. Traveling on separate tickets and unrelated airlines is definitely acceptable and this detail is clearly and without any doubt copied into Timatic that is used by check-in staff.

When you land in Beijing the first thing you will do is to approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit by presenting your flight tickets. After a short check, you will be granted a permit and you will head to the immigration. When you have cleared the immigration you will collect your luggage and perform new check-in to your final destination at the time written on your Korea bound ticket. Have a nice journey.