Remember that 断つ means "to cut [off]", which carries the connotation of "put an end to", i.e. discussions or other progressing concepts.
A related word is 断言 which means, more or less, "the final word", or "an authoritative answer". Often used in a negative context when searching for a tactful dodge: 「断言できないね」.
So 断定 is then "to set with finality", while 結論 can be "to tie together theory/discussion".
In general it's a good rule of thumb at least with 漢語 to ask first what the characters are saying, and then try to connect that to the meaning.