yes, i believe there is: "not taking care of the horse" is the sentence above - "nestarat se o toho koně", and it means that you don't feed him enough and you don't clean his stable "not caring about the horse" is "nezajímat se o toho koně" (but you could also translate it as "nestarat se o toho koně"), and it means that the horse is not important to you, you're not interested in him (it's like the sentence "i don't care" - "nezajímá mě to/je mi to jedno")
"Ty se o toho koně nestaráš." - YOU are not taking care of the horse. "Nestaráš se o toho koně." - You are NOT TAKING CARE of the horse. "O toho koně se nestaráš." - You are not taking care OF THE HORSE.
All these examples can be twisted even more by adding stress to a single word. Czech can be complicated like that.
That's interesting. In Russian, Ukrainian, and Polish, the word(s) at the end of the sentence take the emphasis, the opposite of your Czech examples. It would translate as follows (using Czech to avoid other languages):
Ty se o toho koně nestaráš. - You don't take care of that horse.
Nestaráš se o toho koně. - You don't take care of that horse.
O toho koně se nestaráš. - You don't take care of that horse.
In order to emphasize "you," the translation would be something like „O toho koně nestaráš ty.” The apparent redundancy of including ty after the 2nd-person conjugation of the verb nestaráš, especially last in the sentence, is there for emphasis.
This is the standard rule of emphasis in written Russian, Ukrainian, and Polish, when italics, bold, or CAPS are not used for emphasis. Obviously in the spoken languages, vocal intonation emphasizes the words in the sentence.
No, va-diim, your three sentences are right, even in Czech - just like in other Slavic languages. The last word/expression is the important one - the new information, the stressed point.
David_Sarif's examples are only true if you actually speak them with a strong emphasis on the first word - you have to use intonation to make his examples mean what he says they mean.