In general every day use there is no difference in the two expressions. Consider them interchangeable. Strictly speaking, "apt" indicates an "aptitude" meaning an area where one has nature abilities. For example some people are naturally better at mechanical skills than another, or they're a better cook or are better at mathematics than say languages. These are "aptitudes" whereas "tend" indicates a tendency toward doing something. Generally this would be something they like to do regardless of whether they have an aptitude toward it. For instance, some people "tend to sing" when they're happy but that doesn't mean they have an aptitude for singing.

@ Don: They're not the same (you just defined them and their meaning is neither the same nor interchangeable). Kouji, being "apt" at something means it's something you have a natural ability to do well at; When you "tend to do" something, it's just something that you do regularly or semi-regularly; Can also be something that happens regularly or semi-regularly; it's a pattern of behavior or occurrences. "Billy was apt at painting, but he tended to be high most of the time." (Billy was good at painting, but he was usually high most of the time) "The rain is apt at keeping my plants alive, but it tends to rain least in summer when they need it most."

@Maidhc, I don't think I said they are the same, what I said is ordinary use they are used interchangeably. I then defined the differences. If we're going to get nit-picky, in your last example, rain cannot be "apt" to do something. As an inanimate object it has no aptitude. In this instance I'm not sure the word "tend" would be accurate either as water is requirement to keep your plants alive. You can have the last word.