I have a $2000 bike and I do ride on trails. Please do not use the word "Bicycle" and the word "Wallyworld" in the same sentence in my presence!
Just kidding, but yes, there is an enormous difference. Huge. However, that being said, it is better to start out mountain biking with an entry level, under $1000 hardtail. Something like a Specialized Rockhopper, etc. Something for around $800 or so. Buy it at a bike shop, ask a lot of questions, and make sure it is fitted to you. If they don't put you on it, and measure stuff, they are not fitting it to you--take your business somewhere else. Do not buy a bike from a shop that will not take time with you, fit it to you, and offer you some sort of free tuneups for a year, or other perk. If they are all arrogant and snobby because you are a newby, go somewhere where they appreciate your business.
Dang I hate snobby little bike shop pr*cks...there are some nice guys in the business, though.
Then go ride trails, and ride WITH other riders who are better and are willing to teach you some skills. Don't let them take you anywhere super steep and try to kill you-- find out which single track trails are rated beginner and ride those, then move to beginner/intermediate and ride those, then on to solid intermediate, etc.
Canal roads don't count as beginner, by the way. Ride them anyway, just for pedaling exercise! Ride everywhere, ride to work, ride to school, ride to the store--you will need that fitness for the trails later on. (Buy a really good lock and/or ride your wallyworld bike to the store, though) I actually walk around in the grocery store WITH MY BIKE sometimes.