四つ仮名 is right. I actually looked into this in some detail, previously, because it made no sense that there were two sounds with two different representations, in a very recently reformed writing system. The truth is that there are not, of course.
The full situation is a little more complex than @Leebo wants to make out, but the simplified version is that modern Japanese is undergoing a merging of four separate morae into one (that’s right, じ、ぢ、づ、ず all representing one sound), to varying degrees across the country.
Older, careful speakers will often distinguish, even if they are not consciously doing so, but for most speakers, depending on their area, one of the following is true:
ず、づ are allophones and じ、ぢ are allophones - this is typical of Tokyo and much of central Japan, which is where most Japanese live, of course. This is also the accent and dialect usually taught to learners as “Standard Japanese”.
ず、づ、じ、ぢ are all allophones - this is the most extreme case, and it is found in Hokkaido and the north of Japan, as well as the far south, including Okinawa.
じ、ぢ are allophones (the other two remain distinguished) - this is a small pocket in southern Japan.
No allophones (all morae are distinguished) - this is common in much of southern Japan.
Allophones are where different sounds are realized (and heard) by native speakers as being the same sound. For example, in English, people realize vowels like /e/ and /i/ in a variety of different ways, whilst still having no confusion over which vowel is being used. Likewise, /l/ has several allophones across English.
What this means for us, as learners, is that we may very well hear these sounds distinguished from one another, even in dialects where they have merged, to one extent or another, but that for the most part we shouldn’t attempt to make an explicit difference ourselves, unless we are very sure.
In most cases, the native speaker is not even going to be aware that they make two different sounds for the same kana, similar to the /g/,/ng/ allophones situation with が、ぎ、ご、etc.
@Leebo native speakers without some expertise are a terrible source of information on things like this; unless they have chosen to analyse their own speech, they are not going to be able to given accurate feedback. You will simply get blanket statements like “they are the same sound”, even as they proceed to make two different sounds for it (allophone).