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Those two models are very different in both the underlying assumptions and the specifications. The first one is a SAR model which assumes that the errors are multivariate normal distributed, hence, no iid observations, and thus, the likelihood function is different from what you would observe in a plain OLS. Also, the spautolm includes the autocorrelation term when you specify listwd, so, if discrep_net_prop_more.W is your exposure terms, it means that you are including it twice but in the wrong way. Instead, you should type something like:
spautolm(formula = BLQFMHEDWM.W ~ 1, listw = w.list.trunc,
family = "SAR", zero.policy = TRUE)
For example. The autocorrelation term is the Lambda coefficient which is reported afterward.
The lm, on the other hand, runs an OLS model in which the errors are assumed to be iid making that type of model (including an exposure term) not valid as your estimates will be biased by construction (unless you are using a lagged exposure). A good reference on spatial econometrics is here:https://www.cairn.info/resume.php?ID_ARTICLE=REI_123_0019