There's no difference in meaning. But the second sentence is "spelt out" more, to make it easier for some people to understand. So, if I'm speaking to a non native English speaker, or someone with poor hearing ability, and I say the first sentence and they don't understand, I might then say the second sentence, instead of repeating the first - to say it in a slightly different way and to spell it out more, for maximum chance that they may understand me.

The difference between these two sentences is quite subtle and mainly involves the structure and emphasis: "Don't take for granted the things closest to your heart!" This sentence is more direct and concise. The phrase "things closest to your heart" functions as a compound adjective ("closest") describing "things," with "closest" modifying "things" directly. It focuses on the concept of "things" that are emotionally important, without additional clarification. "Don't take for granted the things that are closest to your heart!" This version is slightly more formal or explicit. The phrase "that are closest to your heart" adds an extra layer of description, using a relative clause ("that are closest to your heart") to clarify which "things" are being referred to. It's a bit more detailed, emphasizing that the "things" being discussed are specifically those that have a deep emotional connection to you. In essence, both sentences convey the same core idea, but the second sentence provides a bit more explanation, while the first is more streamlined.