we cut down on our budget

We have problems making ends meet; it's time we cut down on our budget.
...                                                                  we cut down our budget.


Hi,
Do both of the above sound right and mean about the same to you? Thanks.

This is a good question. We do say "cut back on our spending" but why can't we use "on" when it comes to expenses? With and without sound equally good to my learner ear. I hope there's an explanation.