The preservation of maximum diversity within the smallest number of accessions is one of the challenges of germplasm management, and the assessment of the population structure, the relationships between the accessions, and the construction of core collections are the key steps. The choice of suitable molecular markers is often the starting point. In this study, we analyzed a part of the INRAE walnut germplasm collection, which is highly diverse and unique in Europe, consisting of 150 accessions from American, European, and Asian continents. Based on genotypic data already available, using 13 SSRs or 364,275 SNPs, we showed that the first level of structure is detected equally. We also highlighted empirically that approximately 100 SNPs are needed to obtain similar clustering to 13 SSRs in Principal Coordinate Analysis (PCoA). We constructed eight core collections following two strategies (percentage of total allelic diversity or number of accessions) and two construction methods based on different algorithms ("maximum length subtree" and "entry-to-nearest-entry" methods). We showed that core collections based on few SSR markers are able to capture at least 99.5% of the SNP allelic diversity, irrespective of the construction method used. Then, core collections based on each marker type are highly similar, using both construction methods. All these steps are crucial to identify the suitable tools and methods to improve plant genetic resources management.