Learn English – “Start work” vs “start working”

There can be a subtle difference.

If I were creating something, e.g. writing some new programming code; putting some electrical or mechanical components together to achieve a particular objective; installing and setting up a new TV set for the first time ^[1]; then, if unsuccessful, I might say "I didn't get it to work" or "I can't/couldn't get it to work" ^[1]. (It had never worked, because it was new.)

If I were repairing something that had previously worked (e.g. repairing a previously working TV set ^[1]) and the repair was unsuccessful, then I would probably say "I didn't/can't/couldn't get it working". (It had previously worked.)

Note that these are subtle differences, and I do not mean to imply that the expressions and scenarios are necessarily always used that way around, not that it would be wrong to use them the other way around.

_{^[1] Thanks to Janus Bahs Jacquet, whose comments contributed some examples and other input to my revised answer.}

They technically mean the same thing (and both are grammatically correct).

There is a difference, but it is subtle. It's more clear in spoken English, or at least easier if you add an emphasis where necessary (which I have done below).

It works.

Plain and simple, the thing works; no implications here.

It actually works.

Think of it more as "You would think it wouldn't work, but it works." Perhaps other products in the same category don't work, and this dispels any disbelief in the product's ability to work.

Alan: This application does not work!
Bob: It actually does work, but you need the latest JVM installed.

Even more emphasis on the fact that you think it wouldn't work, but it does.

And if you want to add even more emphasis (but is on the brink of grammatically incorrect, and overuse of this might lead people to stop taking you seriously):

It really does actually work.