The phoneme /dz/ is purely alveolar, whereas /dʑ/ is alveolo-palatal. The voiceless equivalents (and the more common IPA versions) are /ts/ and /tɕ/, as further explained on that same page.
The palatal consonants are pronounced with the middle of the tongue (the body) raised toward the hard palate. Hence it feels like more "middle of the mouth" than the pure alveolar or dental "front of the mouth" consonants.
The comparison to English beds /bɛdz/ and gee /dʒiː/ is not bad, as an approximation.
How does that work for ㅈ ? In the standard Seoul-based Korean, it is to do with what vowels follow it: /dz/ is the sound before the back vowels ㅏ, ㅓ; the more palatal version /dʑ/ is used for other vowels. In North Korean, /dz/ seems to be used before more of the vowels, and /dʑ/ only before the front vowel ㅣ and iotated vowels (ㅑ, ㅕ, ㅠ, etc.).
But this difference is not as strong for ㅈ, in contrast to ㅅ.
Compare 하자 (haja) with 하지 (haji). In the modern standard Seoul-based Korean pronunciation, both are somewhat palatal, although palatalisation is stronger (as in, the tongue goes further up/back) with the latter.
Now compare the difference in 도사 (dosa) with 도시 (dosi). The ㅅ sounds very different between the two: the first one is definitely an alveolar /s/, whilst the second one is an alveolo-palatal /ɕ/, closer to the English "sh".