I think "Baby Hawks," (the moniker that people were using in pre-season) is closer, with the addendum that the Celts are playing defense like the Bucks last year, or the Heat during their championship runs. Aggressive, attacking passing lanes, thriving by forcing tons of turnovers.
Comparisons to the Spurs always break down when we recall that unlike the Spurs, the Celts entirely lack elite scoring options, and particularly lack big men with the ability to take advantage of individual matchups inside.