How is it possible that phylogenies based on sequences from nuclear genomes and organellar genomes (i. e., chloroplasts and mitochondria) from the same group of species yield phylogenetic trees with different branching orders?

From the sequence, we can only tell the percentage similarity between the genome sequences, however, the ambiguity arises from the various sequences of possible modifications in the genomic sequences. For example in a conserved genomic seqence CAGGGCCC, some organisms have this sequence and other organisms have the sequence CAGGACCC, In this case, it is fairly straightforward to say that the latter group evolved from the former group with a modification in the G base to A base. Similarly if another group arises with the sequence CAGGACTC, it is also probable to say that this group arised from the CAGGACTC group with an additional modification.

However, who's to say that the CAGGACTC group did not evolve first and the mutation from C to T base evolved later. If so, then the order of branches on the tree would change. This is just one example of the ambiguity that can arise from determining the order of genomic sequences mutation to determine the order of evolution.

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