～る所(ところ)だAbout to, On the verge of

Both can describe actions about to happen, but with different nuance. るところだ simply states that something is on the verge of occurring. Verb[volitional] + とする adds a sense of intent or effort, and is often used when the action may not actually happen, e.g. 子どもはなんでも食べようとする ('Kids will try to eat anything.'), where 食べるところだ wouldn't be appropriate.

たところだ and るところだ share the same structure, with the tense indicating whether the action is complete or not. るところだ uses the non-past form to mean 'about to do' something, e.g. 晩ご飯を食べるところだ ('I'm just about to eat dinner.'). たところだ uses the past form to mean 'just did' something, e.g. 晩ご飯を食べたところだ ('I just ate dinner.').

ところだ and かけ both express incomplete actions, but with a key difference. るところだ emphasizes that the action is just about to happen, e.g. リンゴを食べるところだ ('I'm about to eat an apple.'). かけ indicates the action has started but isn't finished, e.g. 食べかけのリンゴ ('a half-eaten apple').

るところだ and ところだった① both express that an action is or was about to happen, but differ in outcome. るところだ means the action is about to occur and likely will. ところだった① means it was on the verge of happening, but didn't in the end.