Hmm, are you sure that they're synonymous? I initially assumed that your post was talking more about holistic vs. analytical reasoning (see e.g. pages 23-27 of The Weirdest People in the World), which seems to have some similarities with System 1/System 2 reasoning, but also differences which don't map so clearly to it:

Holistic thought involves an orientation to the context or field as a whole, including attention to relationships between a focal object and the field, and a preference for explaining and predicting events on the basis of such relationships. Analytic thought involves a detachment of objects from contexts, a tendency to focus on objects’ attributes, and a preference for using categorical rules o explain and predict behavior. This distinction between habits of thought rests on a theoretical partition between two reasoning systems. One system is associative, and its computations reflect similarity and contiguity (i.e., whether two stimuli share perceptual resemblances and co ‐ occur in time); the other system relies on abstract, symbolic representational systems, and its computations reflect a rule ‐ based structure (e.g., Neisser 1963, Sloman 1996).

Although both cognitive systems are available in all normal adults, different environments, experiences, and cultural routines may encourage reliance on one system at the expense of another, giving rise to population ‐ level differences in the use of these different cognitive strategies to solve identical problems. There is growing evidence that a key factor influencing the prominence of analytic vs. holistic cognition is the different self ‐ construals prevalent across populations. First, independent self ‐ construal primes facilitate analytic processing, whereas interdependent primes facilitate holistic processing (Oyserman & Lee 2008). Second, geographic regions with greater prevalence of interdependent self ‐ construals show more holistic processing, as can be seen in comparisons of Northern and Southern Italians, Hokkaido and mainland Japanese, and Western and Eastern Europeans (Varnum et al. 2008).

Furthermore, the analytic approach is culturally more valued in Western contexts, whereas the holistic approach is more valued in East Asian contexts, leading to normative judgments about cognitive strategies that differ across the respective populations (e.g., Buchtel & Norenzayan, in press). Below we highlight some findings from this research showing that, compared to diverse populations of non ‐ westerners, Westerners (1) attend more to objects than fields; (2) explain behavior in more decontextualized terms; (3) rely more on rules over similarity relations to classify objects; (for further discussion of the cross ‐ cultural evidence Nisbett 2003, Norenzayan et al. 2007).

(E.g. this difference wouldn't seem to be something that you'd expect to arise from just System 1/System 2 processing:)

Several classic studies, initially conducted with Western participants, found that people tend to make strong attributions about a person’s disposition, even when there are compelling situational constraints (Jones & Harris 1967, Ross et al. 1977). This tendency to ignore situational information in favor of personality information is so commonly observed—among typical subjects—that it was dubbed the “fundamental attribution error” (Ross et al. 1977). However, consistent with much ethnography in non ‐ Western cultures (e.g., Geertz 1975), comparative experimental work demonstrates differences that, while Americans attend to dispositions at the expense of situations (Gilbert & Malone 1995), East Asians are more likely than Americans to infer that behaviors are strongly controlled by the situation (Miyamoto & Kitayama 2002, Morris & Peng 1994, Norenzayan, Choi et al. 2002, Van Boven et al. 1999), particularly when situational information is made salient (Choi & Nisbett 1998). 6 Grossmann et. al. provide parallel findings with Russians (Grossmann 2008). Likewise, in an investigation of people’s lay beliefs about personality across eight populations, Church et al. (2006) found that people from Western populations (i.e., American and Euro ‐ Australian) strongly endorsed the notions that traits remain stable over time and predict behavior over many situations, while those from non ‐ Western populations (i.e., Asian ‐ Australian, Chinese ‐ Malaysian, Filipino, Japanese, Mexican, and Malay) more strongly endorsed contextual beliefs about personality, such as ideas that traits do not describe a person as well as roles or duties, and that trait ‐ related behavior changes from situation to situation. These patterns are consistent with earlier work on attributions comparing Euro ‐ Americans with Hindu Indians (see Shweder and Bourne (1982) and Miller (1984)). Thus, although dispositional inferences can be found outside the West, the fundamental attribution error seems less fundamental elsewhere (Choi et al. 1999).