The fundamental difference is that there is a fixed bi-univocal (one-to-one) relationship between an index and its referent, whereas there is no such relationship between a signifier and a referent or between a signifier and a signified.
In the seminar of 1958-9, for example, when presenting the elementary cell of the graph of desire, he designates one point as the code, which he also designates as the place of the Other and the battery of signifiers.
Somebody spent some time this afternoon trying to convince me that it would surely not be a pleasure for an English-speaking audience to listen to my bad accent and that for me to speak in English would constitute a risk for what one might call the transmission of my message. Truly, for me it is a great case of conscience, because to do otherwise would be absolutely contrary to my own concept of the message: of the message as I will explain it to you, of the linguistic message. Many people talk nowadays about messages everywhere, inside the organism a hormone is a message, a beam of light to obtain teleguidance to a plane or from a satellite is a message, and so on; but the message in language is absolutely different. The message, our message, in all cases comes from the Other by which I understand "from the place of the Other." It certainly is not the common other, the other with a lower-case o, and this is why I have given a capital O as the initial letter to the Other of whom I am now speaking.