You pays your money and you makes your choice - context is everything.
'I need something doing' - I have an issue for which I am responsible, and something needs to be done to resolve it, e.g. I need the brakes doing. Doesn't say by whom, might be me, might be someone I'm paying. Think of it as a precursor to a further statement that might take the process further.
'I need something <to be> done' - the infinitive that makes it a declarative statement strictly should be present but is often elided. You're simply stating that, in your opinion, something must be done.
English is wonderful for subtle contrasts in meaning. In both cases, you're referring to the time at which the event might take place; in the first continuous tense, there's a hint of some sort of ongoing process, while the second implies a wish that you want it *to have been* done; you want to look at it from the future and see it completed.
In practice, that difference is one so subtle as not to exist for most people and as you say, they're interchangeable.
Something needs doing is just a reordering of the words in the first phrase - English isn't particularly positional - and has the same meaning.
The Scots version is perhaps a clearer expression of the difference in the second - there is an elided but implicit infinitive there: something needs <to be> done.
Though of course you can then wander into the realm of metameaning: what is this object that has needs? Let's not go there.
On the other hand, the recent habit of starting explanations and declarative statements with 'So...' is an abomination unto Nuggan! And don't even get me started on 'ahead of' when 'before' is meant.