Trademarks and copyright have entirely different purposes. Corporate logos are often both.
A trademark is a brand, it identifies your work. Apple puts its logo on its computers to show that they made them. Because it is a registered trademark, you can't put the Apple logo on your own computers because it will mislead people into thinking they are Apple products. However, it doesn't prevent you from using the Apple logo in any other way. You can make artwork featuring the Apple logo if it is clear that Apple have nothing to do with it. If you keep your trademark registered and actually use it, it will never expire.
Copyright is about protecting the work of the artist or the company that commissioned it. For example, making a nice logo is hard work and you want to be compensated for it, so you may want people who use it to pay you, that's what copyright is for. The Apple logo precise shape, colors, etc... are covered by copyright. It means that you can't reuse the art for any reason without permissions, so in that way, it is a stronger protection than a trademark. The idea of a bitten off apple is not covered by copyright however, copyright doesn't cover ideas, only actual work, so if it wasn't also a trademark, you could have put your own drawing of a bitten off apple on a computer you made. Copyright doesn't need to be registered and expires after about 100 years.
The third category, also different, are patents. Patents protect inventions, I don't think it makes sense to patent a logo, but I can imagine a tiling shape being patented. Or more precisely, the practical application of such a shape. Patents need to be registered and meet certain criteria, they expire after 20 years.
A trademark is a brand, it identifies your work. Apple puts its logo on its computers to show that they made them. Because it is a registered trademark, you can't put the Apple logo on your own computers because it will mislead people into thinking they are Apple products. However, it doesn't prevent you from using the Apple logo in any other way. You can make artwork featuring the Apple logo if it is clear that Apple have nothing to do with it. If you keep your trademark registered and actually use it, it will never expire.
Copyright is about protecting the work of the artist or the company that commissioned it. For example, making a nice logo is hard work and you want to be compensated for it, so you may want people who use it to pay you, that's what copyright is for. The Apple logo precise shape, colors, etc... are covered by copyright. It means that you can't reuse the art for any reason without permissions, so in that way, it is a stronger protection than a trademark. The idea of a bitten off apple is not covered by copyright however, copyright doesn't cover ideas, only actual work, so if it wasn't also a trademark, you could have put your own drawing of a bitten off apple on a computer you made. Copyright doesn't need to be registered and expires after about 100 years.
The third category, also different, are patents. Patents protect inventions, I don't think it makes sense to patent a logo, but I can imagine a tiling shape being patented. Or more precisely, the practical application of such a shape. Patents need to be registered and meet certain criteria, they expire after 20 years.