With climate change impacting trees worldwide, enhancing adaptation capacity has become an important goal of provenance translocation strategies for forestry, ecological renovation, and biodiversity conservation. Given that not every species can be studied in detail, it is important to understand the extent to which climate adaptation patterns can be generalised across species, in terms of the selective agents and traits involved. We here compare patterns of genetic-based population (co)variation in leaf economic and hydraulic traits, climate–trait associations, and genomic differentiation of two widespread tree species (Eucalyptus pauciflora and E. ovata). We studied 2-year-old trees growing in a common-garden trial established with progeny from populations of both species, pair-sampled from 22 localities across their overlapping native distribution in Tasmania, Australia. Despite originating from the same climatic gradients, the species differed in their levels of population variance and trait covariance, patterns of population variation within each species were uncorrelated, and the species had different climate–trait associations. Further, the pattern of genomic differentiation among populations was uncorrelated between species, and population differentiation in leaf traits was mostly uncorrelated with genomic differentiation. We discuss hypotheses to explain this decoupling of patterns and propose that the choice of seed provenances for climate-based plantings needs to account for multiple dimensions of climate change unless species-specific information is available.