The Lumia 625 does not support native SDXC but SDHC which is compatible with SDXC. Secondly the article Wpcentral posted was in March early this year, 128 GB cards are SDXC and weren't launched till MWC early this year. Wpcentral posted a follow up article after a few weeks that the 521 with 8.1 works with the 128 GB cards. In between these two articles there was another article stating that Nokia has started acknowledging support for the 128 GB cards atleast for the Lumias that launched with 8.1 (newer models). So it might be that 8.0 won't be able to see the 128 GB card on the previous gen models till 8.1 was launched? Or may be due to unavailability no one was able to test it? The 1520 is a newer model (new generation) and hence it was able to see it? I haven't seen anyone confirm that the previous gen models were able to use the 128 GB cards while on 8.0, I've used 64 GB SDXC on 8.0 and it seemed to work fine
Micro SDHC is NOT compatible with SDXC. SDHC supports only up to 32gb memory. SDXC supports above 128gb.
Any phone that supports up to 64gb cards is by default, having an SDXC slot. The Lumia 625 is marketed as having expandable memory up to 64 GB at the time of release as 128 GB cards were not discovered then. The Lumia 520,525,530,620,625,630,720,820,1320,1520 all have SDXC slots. For confirmation, please refer to this article-http://en.m.wikipedia.org/wiki/Secure_Digital