Flight 634 LAS-PHL at 0645 was most likely "US Air 634" on those dates, while flight 634 LAS-PIT at 2257 was most likely "America West 634" on those dates. Even if both were to have flown with the ATC callsign "Cactus 634," that wouldn't be a problem for ATC since they were separated in time by several hours. (No more an issue than N12345 flying KABC to KABC more than once in a day.) But most likely, they flew with separate callsigns too, as explained below.
Why is this the likely answer?
The LAS-PHL flights in the OP were flown by aircraft whose registrations end in "AU" such as N628AU for example. The airfleets website shows that this aircraft was a US Air (later, US Airways) jet until it was re-registered in December 2006 (the dates on that site are DD-MM-YYYY format). Generalizing from that example, these jets were legacy (pre-merger) US Airways jets.
The LAS-PIT flights in the OP were flown by aircraft with registrations ending in "AW" such as N810AW. Airfleets shows that this was an America West jet until it became a US Airways jet in October 2006. Again generalizing from this example, the "AW" jets were "American West" aircraft at the time of the OP's data.
So at the time, the one flight was being flown by jets in US Airway livery, and the other by jets in America West livery. And to the passengers, they almost certainly were sold under the respective brands, so one could buy a ticket for "US Air flight 634" from LAS to PHL in the morning, or a ticket on "America West flight 634" from LAS to PIT in the evening. You'd have to use two separate websites to do so, but there would be no confusion.
Okay, so the remaining question:
Why do they both have the "US" (presumably meaning US Air)
uniquecarrier ID in the table?
As described in this paper from Embry Riddle Aeronautical University,
America West Airlines acquired the bankrupt US Airways on September 27, 2005
to form the US Airways Group.
The two airlines became fully one in 2007, when a single operating certificate covered them both. During the interim,
Both of the merged airlines retained their names and continued operating until September 25, 2007, when America West's FAA certificate was merged into US Airways.
This interim period is when the flights shown in the OP occurred. At this point, the airlines were in the process of merging their operations, although their website weren't merged until May 2006. Thus, in the January/February timeframe posted, the tickets for each would be sold separately.
The wikipedia article notes that the callsigns remained separate until 2008, as "US Air" and "Cactus"; after October 2008, the entire operation used "Cactus".
While it's hard to retrace each step along the way from two separate carriers to one unified carrier, it's clear that various steps are involved, so it seems probable that whatever data source gives the
uniquecarrier identifier in the table, either switched over separate identifiers before the dates of these flights, or else it was retroactively changed over to make them all "US" even though at the time some would have been "AW".
In the general case...
So, is it possible, to have two flights with the same number at the same airport at the same day? Yes, although the data shown above probably doesn't indicate that LAS saw a "US Air 634" twice a day during the timeframe shown. But as long as the first flight and the second don't overlap in time, there is no ATC constraint that prohibits is. (Military aircraft do this all the time... Cool06 can fly from KDLF to KDLF on a training mission multiple times during the day -- Laughlin AFB in this case.) It's possible, but sufficiently unwise because of the potential to create confusion, that it probably happens for an airline somewhere between very rarely, and never.
As a matter of avoiding confusion, an airline would probably work to avoid scheduling their flight 123 more than once in a day:
"I'm here for my flight 123."
"Sorry, but YOUR flight 123 isn't for another 10 hours; this is the other flight 123 today."
But, if flight 123 is scheduled to depart at 2300 and one day it runs over an hour late, the next calendar day will have two "Flight 123" operations, and nothing will break.
All that to say, what the data in the OP most probably shows, is an artifact of how US Air operated during the transition from two airlines into one, and may not really be particularly indicative of anything more widespread, nor generalizable, than that.