The last job I had made you apply for SSDI before giving you LTD. Then they paid anything over what SSDI did to hit the 60%. It still would have been nearly double what I get from SSDI (I hadn't worked there long enough to get LTD). Just telling you b/c it was a surprise to me.
Another thing I learned was to apply for SSDI as soon as you think you need it. You can always cancel later. I had to be hospitalized because I wanted to kill myself rather than face the realization I was done working. When I got out I didn't apply for 2 months, partly because I thought I'd get LTD through my company and partly because I was still in denial. But those 2 months would have made a difference because I wouldn't hav run out of STD before approval if I had been approved as fast as I was with my actual submission date.
Sometimes the underwriters can be strange. I had one policy for STD that called me and said they couldn't cover everything. I thought "here goes bipolar and my ability to keep this job". Instead they excluded a completely harmless health problem that never would make me miss a day of work.
That's about all I know. If you ever need STD it can be a fight, not because you don't deserve it or have done something wrong, but because they make it hard. My pdoc called a company and completely chewed them out once after they left me hanging without income for 6 weeks. She told them that they were stressing me out and she would be keeping me out longer the more stress they put me under. She won that fight