You pay into STD to receive it, it's like insurance for broken body parts, pregnancies, etc.. Things that don't last 12 weeks or more, long-term disability kicks in after that. Most companies have an automatic LTD plan.
All companies have varying policies. As mentioned above, most require you draining all of your sick time first if vacation PTO is in a different bucket, or all PTO if not. Other companies allow you to only to withdrawal after a waiting period. My company offers 2 premiums for two different waiting periods, 14 and 28 days. Before kids, I had 12 weeks of sick time acquired and was able to stop paying into STD all together while still keeping pay secured.
PRDATR, Call your HR rep and they should get you squared away. I'd think they want you taken care of so you can get back to a full recovery, and work. Good luck healing.