Both Calvinists and Arminians believe that as a result of sinful nature inherited from Adam, man left to his own devices lacks the will or ability to repent and turn to God. Both believe that God must first act in order for man to respond. Both believe in the doctrine of Total Depravity and inability.
Some Calvinists such as John MacArthur have misrepresented Arminians in saying that Arminians believe that "the sinner unaided by the Holy Spirit must make the first move". Fortunately there are still some Calvinists out there who make the effort to accurately portray those who have opinions different to their own.
Where the two systems part is in the remedy to this problem of inability. Arminians teach that God works through Prevenient Grace in order to enable sinners to respond. Calvinists teach that God first makes a sinner born again, and then the sinner can only choose to repent, and in fact cannot choose not to repent. The difference is in whether God allows his grace to be resistible or not.
Calvinists such as John Piper have said that Arminians don't believe in Total Depravity as Calvinists do. A quote from Piper (which can be found at 4:45 in this video) says "Calvinism says people are so depraved and rebellious that they're unable to trust God without a special work of grace to change their hearts so that they necessarily and willingly believe. In other words if this grace doesn't compel them to believe they won't believe." (As a side note, I do appreciate Piper's honesty in saying that Arminians believe in the necessity of grace to believe, given that misrepresentation in this area is so rampant by many.)
If the above is how the Calvinists specifically define Total Depravity, then there is a difference between the two camps (not that Calvinism should be the benchmark for the term in the first place). To the Arminian, the difference isn't in the Depravity. It's not that we believe we are "less totally depraved" than Calvinists do. The difference is in God's power. Does God have the ability to enable a sinner to repent who is totally depraved, without having to do so irresistibly? Arminians such as myself say God could act irresistibly, (though he decides to do otherwise.) It seems the real difference between the views is that Calvinists limit God's power in saying that God is unable to enable a sinner without acting irresistibly.