Is illegal downloading a victimless crime?
No it is not a victimless crime because while your internet provider keeps your information private, your personal IP address is traceable and you can be brought to legal action should a firm or company find that you are downloading property that you did not own the rights to. Also, while downloading may seem harmless and easy, it does affect not only the artists/actors/authors/publishers/etc, it also affects the companies that offer to sell the media.
Is illegal downloading different from stealing, if yes why/how is it different?
While illegal downloading is not a physical act of stealing, it is not any different as you are taking something that you did not pay for. Media is the intellectual property of the artist/actors/authors/publishers/producers/etc and downloading it illegally is exactly the same as stealing in my honest opinion. And while there are websites that offer “free downloads,” they typically just send you to an external website in order to avoid any legal repercussions.