  The J-region asymptotic giant branch (JAGB) method is a new standard candle
that is based on the stable intrinsic J-band magnitude of color-selected carbon
stars, and has a precision comparable to other primary distance indicators such
as Cepheids and the TRGB. We further test the accuracy of the JAGB method in
the Local Group Galaxy M33. M33's moderate inclination, low metallicity, and
nearby proximity make it an ideal laboratory for tests of systematics in local
distance indicators. Using high-precision optical BVI and near-infrared JHK
photometry, we explore the application of three independent distance
indicators: the JAGB method, the Cepheid Leavitt Law, and the TRGB. We find:
$\mu_0$ (TRGB I) = 24.72 +/- 0.02 (stat) +/- 0.07 (sys) mag, $\mu_0$ (TRGB NIR)
= 24.72 +/- 0.04 (stat) +/- 0.10 (sys) mag, $\mu_0$ (JAGB) = 24.67 +/- 0.03
(stat) +/- 0.04 (sys) mag, $\mu_0$ (Cepheid) = 24.71 +/- 0.04 (stat) +/- 0.01
(sys) mag. For the first time, we also directly compare a JAGB distance using
ground-based and space-based photometry. We measure: $\mu_0$ (JAGB F110W) =
24.71 +/- 0.06 (stat) +/- 0.05 (sys) mag using the (F814-F110W) color
combination to effectively isolate the JAGB stars. In this paper, we measure a
distance to M33 accurate to 2% and provide further evidence that the JAGB
method is a powerful extragalactic distance indicator that can effectively
probe a local measurement of the Hubble constant using spaced-based
observations. We expect to measure the Hubble constant via the JAGB method in
the near future, using observations from JWST.
