Both regular season and playoffs are played on the same courts, with the same balls and same baskets. Also, most of the rules are the same. Therefore, teams performance during the season is usually pretty good indicator of how they would fare in the playoffs. The better team typically has higher seed and will more often than not win a series against a lower seed.
There are however differences which should not be ignored:
1) Shortened rotations a.k.a. starball. Teams tend to rely on their stars more heavily during the playoffs. The stars play more minutes than during the regular season, and end of the bench never plays except during blowouts.
2) Increased favoritism toward the stars a.k.a. refball. The playoffs is when the NBA is heavily promoting its stars. Whole NBA ad machine is promoting stars at the expense of the teams all the time, but especially during the playoffs. When two closely matched teams meet in the playoffs, the refball can decide, which team goes forward.
3) Most NBA teams have a lot of soap opera going on during the regular season. The players and coaches often pay more attention to details of internal politics, contracts, minutes, etc. than to the team record. So most teams underperform during regular season and only reach their full potential in the playoffs.
If you think about these factors, you’ll see there are reasons why the Spurs are an exceptional regular season team. Of course, they can still win in the playoffs against teams that are not so good. But a few NBA teams that have more talent and can play their stars for 40+ minutes in the playoffs will have an advantage in a 7-game series.