In one case you have mutations - changes - happening to DNA in a random process independent of reproduction. Radiation whatever.
In the other case you have mistakes made in the replication of the DNA.
How is this difference arbitrary?
Because these aren't 2 different cases. Virtually every single instance of a mutation of any kind, point, inversion, duplication, deletion is the result of the process of DNA replication. When mutagenic factors alter DNA they frequently only affect 1 strand and the alteration they produce is frequently not a chemical conversion of a nucleotide to a totally different valid nucleotide but to a particularly chemically altered form of the original nucleotide or an aberant form of a different nucleotide (
Alberts, et al, 2002).It is only when the DNA is copied and a new strand syntesised using the altered nucleotide as a template that a proper complementary nucleotide is introduced into the base pair, and only after a subsequent round of reproduction that a double strand will be produced with 2 properly complementary normal nucleotides.
Arguably retroviral insertions don't require DNA synthesis, at least on the part of the host cell, but in the almost all classes of mutation rely on DNA synthesis, or replication, to effect a valid change in the coding sequence.
That is why your distinction is arbitrary, because the processes you categorise in 1, 'radiation whatever', are also the result of your category 2 'mistakes made in the replication of DNA'.
TTFN,
WK