It's close, but not identical I think. When using always it'll usually mean (almost) every time they meet, but when using all the time it will normally be e.g. one long meeting when she just keeps on giving him notes. But I do agree that in general usage these words are sometimes used interchangeably.
BTW Your sentence is closer to Zij geeft hem de hele tijd briefjes.
Edit: or what Simius said…I think my explanation is closer to what the dictionary says, his explanation closer to how people use the language. :)