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Progress in the three-dimensional modeling of supernovae (SN) prompts us to revisit the supernova remnant (SNR) phase. We continue our study of the imprint of a thermonuclear explosion on the SNR it produces, that we started with a delayed-detonation model of a Chandrasekhar-mass white dwarf. Here we compare two different types of explosion models, each with two variants: two delayed detonation models (N100ddt, N5ddt) and two pure deflagration models (N100def, N5def), where the N number parametrizes the ignition. The output of each SN simulation is used as input of a SNR simulation carried on until 500 yr after the explosion. While all SNR models become more spherical over time and overall display the theoretical structure expected for a young SNR, clear differences are visible amongst the models, depending on the geometry of the ignition and on the presence or not of detonation fronts. Compared to N100 models, N5 models have a strong dipole component, and produce asymmetric remnants. N5def produces a regular-looking, but offset remnant, while N5ddt produces a two-sided remnant. Pure deflagration models exhibit specific traits: a central over-density, because of the incomplete explosion, and a network of seam lines across the surface, boundaries between burning cells. Signatures from the SN dominate the morphology of the SNR up to 100 yr to 300 yr after the explosion, depending on the model, and are still measurable at 500 yr, which may provide a way of testing explosion models.