Rather a lot of possibilities:
Both will use an industry specification test barrel and chamber / freebore length, SAAMI (US) and CIP (EU). They might, or then again might not, be slightly different, resulting in differing pressures, but in any event no two barrels perform the same and produce identical pressures.
SAAMI and CIP use same technology (electronic Piezo crystal) pressure measuring kit, but in different ways which give different results, therefore M.A.P. (maximum average pressure) ceilings; 380 MPa / 55,114 psi and 430 MPa / 62,366 psi respectively in the case of 223 Rem. Incidentally, NATO uses the CIP method and the 5.56 NATO specification is for the same MAP as the CIP 223. In practice, there isn't as much difference as the 7,000 psi bald figure suggests, but Viht is in any case working to different standards from Hornady which may affect load advice data at the margins.
Without looking up my most recent printed Hornady manual, I don't know how many bullets that data apply to, but this company has a serial habit of producing a single common table for up to 15 different bullet models in a modest weight range in a single table. The lowest (pressure) common denominator rule applies, ie in this case results are determined by the model producing the highest pressures of the group with any given charge, and this can understate the safe max of others. Viht uses a single bullet model for each table which is much more precise.
Hornady (again in its print data) uses what in effect is a graphing method of applying maxima linked to MV bands, often in 100 fps steps. Powder A might be spot on the line pressure-wise for say 3,100 fps and that charge weight is shown, but powder B's equivalent step produces 100 psi more than the company has set as its upper limit, so the charge that produces the next step down, in this case 3,000 fps is used. If the steps equate to 1.5gn actual powder weight, the 'loser' might only be 0.1 or 0.2gn 'over' and a lower max charge results.
Different cases and primers in the pressure test cartridges. Such changes can affect results more than most people realise, and do so very much in small cartridges like 223 Rem. That's why loads data says always start low and work up (as well as allowing that chambers and barrels vary between firearms).
Finally, we don't know what assumptions re the max pressure loads each company makes, except in those cases where the test pressure is shown, and neither Viht nor Hornady do so. Viht has a reputation for quoting anaemic maxima, and whilst the company did in some cartridge / bullet combinations at one time, IME its recent 223 Rem max data is 'hot', as in some cases REALLY HOT. The powder companies are in head to head competition over the MVs their powders produce and where PMax values are quoted (as in Hodgdon data), today's maximum loads a are barely shy of industry max - a few hundred psi whereas 10 or 15 years ago, it'd be 2,000 or 3,000 psi. Until recently Viht was struggling in the key US market, and upping its loads to the maximum safe limit may be one way of fighting back to gain market share, or for that matter to simply gain space in reloading manuals. I say may as in so much of this business, you have to speculate, given that nobody gives you the facts. Nevertheless Viht loads simply don't appear for many cartridges in the current crop of US reloading manuals. With lots of choice, the compilers have to omit lots of possibles, and generally it's the lower MV producers that don't get a showing. With everybody including the powder companies using QuickLOAD as a starting / sorting tool, many powders won't even be tested at all if QL results show lower MVs than possible competitors.
