Why did hire me for this competitive salary in the first place? It is just the difference of short term contract and long term contract?
Close but no cigar, this is the differences between being a contractor and an employee.
When you contract you almost never bill 365 days of a year, at least not at the rate you wish you did (bar very few top of the line people who literally have a queue of people begging for their time of day, and willing to pay the asking price). So there's downtime, which is spent looking for more work, and there's never a guarantee that the well won't dry out at any moment. Thus, for all this effort, and risk, and short term availability, contracting tends to pay more. Can be a lot more.
But also you are not really part of the company, you have very little protections and benefits beyond what's in your contract (bar local laws, which may actually strike some of the protections in your contract too, it works both ways - good and bad). You also are unlikely to reap benefit of company success, while in case of sale the C-levels may fight to get all employees paid a bonus, contractors generally just get a firm handshake. Similarly your growth option within the company are going to be limited as you are there to do a job.
On the other hand as employee you are entitled to benefits, protection, stability, growth opportunities and in some form benefiting from the company success you help build. So while the compensation in direct cash tend to be lower, there are other factors to consider; it's nice peace of mind to know that no matter what happens your work life is covered for X months no matter what happens, on top of the savings you got.
To get to your question
Should I consider the same work for 20% less salary?
This isn't the same work, they offered you transition from being a contractor to an employee. And as you've already found it has a downside, as while you got this extension of contract, how likely is the next one is anyone's guess. Maybe you will get another as lucrative after, and maybe you will have to work for half or less of what they are paying you know. No one can know, but that's one of the downsides of contracting.
So what to do?!
Talk with them like you did with us here. Explain that you don't understand the situation, or the difference, why would it be beneficial to take a "pay cut" (I would check the numbers on that too, as contractor you usually have higher tax burden than as an employee, the gap may not be as big as you think) and have an honest and open minded chat. Then make a decision accordingly, but you will have to get your head beyond the numbers, as there's more to what they've offered you.