Technically, grainy is for film emulsion and noisy is for digital sensors. While the causes are quite different, the effects are very similar - especially in low light situations.
But I wouldn't get too worried - a photographer will understand what you mean either way.
There are two additional considerations with digital cameras.
One is tied in very closely with the 'graininess' of an image and it is the physical limitation of the pixel size. On extreme enlargements, this becomes apparent when you can see the picture being made up of lots of blocks of colour - it's called 'pixellation'.
The other consideration is the format the picture is stored in. With the RAW format, it means exactly what the name suggests - every bit of information collected by the sensor is stored. No adjustments. No compression. This gives the absolute maximum image quality possible - but the image files are large.
JPEG files are more commonly used since they have a smaller file size - but they achieve this by compressing the image file in a way which results in 'losing' some of the detail. For the most part, this isn't as big a problem as it may sound. The human eye is also a pixel based image sensor but it has a rather incredible image processor - the human brain. It does some amazing feats of interpretation ....
Take this example:
1. Original Image - Lotsa detail you didn't even know was there!
2. What it was reduced to for the current OzRT 'logo'
3. A close-up look at #2.
Everybody can see #2 is a smaller version of #1 - but people will have difficulty believing #3 is of the same subject, let alone that it is
exactly the same as #2. (If you stand back from you screen 20 feet or more, it will start to look like it though!)
As a result, you can do some pretty severe compression of a full-frame image and, in the right situation, still have a quite presentable picture. Web based photos are a classic.
BUT the truth becomes visible when you start blowing them up....
