Not exactly. Workers comp is limited to illnesses or injuries which are CAUSED BY your employment or a factor thereof. It does not apply to illnesses or injuries which may have manifested themselves while at work but are not caused by your work. The classic example is a heart attack. Even if you are at work when you have the heart attack, it is not eligible for workers comp unless there is verifiable and medical proof that you would not have had the heart attack but for your employment. If you're a truck driver and you're in an accident while driving for the company, that's workers comp. If you're out of state on business and you trip over a chair in your hotel room and break your leg, that's probably not.
How long you have to report the claim and how long you can continue benefits is determined by your specific condition as well as the terms of the policy. MN law appears to set the maximum reporting time as 180 days and the maximum time to collect benefits as 130 weeks, but your specific policy may have shorter periods. As I am reading it, these are the maximum periods a policy is allowed to set, but they are not mandated to set them at these limits. (Workers comp is not my strongest area in the first place - we outsource ours - and I haven't had employees in MN in almost 25 years, so I will gladly accept correction if I am wrong.)
Long term disability benefits generally kick in after any short term or temporary benefits (STD or workers comp) are exhausted. Depending on the policy, it may or may not exclude work-related injuries or illnesses. How long benefits continue is VERY much affected by your specific condition and the terms of the policy. It is not uncommon for Social Security to kick in at 2 years, generally off-setting the LTD benefit.
The important thing to remember, though, is that workers comp vs. LTD (or, for that matter, Short Term Disability benefits either) is not a personal choice. If it is work related, you must go the workers comp route. If it is not work related, you must go the STD/LTD route. The LTD benefits are probably, but not definitely available when/if either of them runs out, but you do not get to choose which is the more advantageous to you; you MUST go with the one that applies.