The 300PPI (which some call DPI/dpi to confuse everyone) is only relevant in connexion with raster images/effects, whereas the (Artboard) size 800x800px (using pixel which some have defined as an actual size identical to a point = 1/72 inch to confuse everyone) actually corresponds to the size 800x800pt.
Therefore the two are quite independent: the 300PPI may apply to artwork of any size, whereas the 800x800pt is the size of the Artboard, which again is part of the Workspace.
A square measuring 800x800pt rasterized at 300PPI will be 3333.3333x3333.3333px (800*300/72).
If you wish to say Argh, it is quite understandable.
This question is one of the most frequent points of confusion asked about in this forum. So I will go ahead and post the answer I typed, despite your having resolved the issue. It may be of benefit to others.
...I have to set the image to 300dpi and 800x800 px...
You have to set what image to those values, and where?
This is a vector-based drawing and design assembly program. Unlike a raster imaging program (Photoshop, etc.) it isn't about just manipulating a single array of pixels. Any program like Illustrator (or like InDesign, etc.) is about assembling any combination of independent OBJECTS into a layout. Each of those OBJECTS can be a raster image, a mathematically-defined shape (vector-based path), or a text object.
So you have to be careful about your terminology when asking for explanations. In the context of a program like Illustrator, the term "image" is assumed to refer to a raster image object. That object may be an individual raster image that exists somewhere on the page, or a rasterization of the entire page that you intend to export, or a raster image that is automatically generated on-the-fly when you apply a raster-based Effect like a Drop Shadow or a Blur. Your question makes it clear that you are confusing all three, and the answer to your question depends on which kind of object you are talking about setting to the required values.
PPI (Pixels Per Inch) is nothing but a scaling factor. 800 x 800 pixels is a specific COUNT of rows and columns of pixels. Any COUNT of pixels can be scaled so as to achieve any PPI. "Pixels" is only half of the equation. "Inch" is the other half.
In other words, you can't know the PPI of a raster image until you know TWO things: The COUNT of rows/columns of pixels contained in the image and the MEASURE of the overall image. Only then can you know the third thing: the COUNT per MEASURE; the Pixels Per Inch:
COUNT / MEASURE=Count Per Measure
So your stated requirements provide two values: 800 is a COUNT of pixels (actually rows or columns) contained in an image. 300 is a COUNT per MEASURE after the image has been scaled to some unknown MEASURE. So:
800/300=Number of Inches
The PPI of an 800 x 800 pixel raster image is 300 PPI only when those 800 pixels (rows/columns) contained in the image have been scaled to occupy 2.66666.... inches. (Notice that this is actually quite intuitive enough to do in your head: How many "threes" does it take to equal one "eight"? Two-and-two-thirds, or 2.6666....)
So whatever 800 x 800 pixel image you are talking about will have to be scaled to MEASURE 2.66 inches in order for its PPI to be 300. That's 2.66... inches or its equivalent in some other unit of actual measure.
Again the question remains: What image are we talking about? And how does that relate to Illustrator's rulers and Document Raster Effects setting? Read on.
Read the first paragraph again and be sure you understand this point: An Illustrator page can contain any number of INDEPENDENT raster images. Each is an independent OBJECT that each can be independently scaled. Therefore, each raster image on an Illustrator page can have its own, individual, PPI value. But Illustrator has only one horizontal page ruler. So there is no way that setting Illustrator's rulers to "Pixels" can reliably indicate
the actual number of pixels contained in any and all raster image(s) that may exist on the page.
Unlike Photoshop, Illustrator's rulers are always an indication of linear measure. A pixel has no linear measure whatsoever until you give it one; i.e.; until you scale it to an actual size. Therefore, a pixel is not a unit of linear measure. So the actual PPI of any raster object that resides on the page, in truth, has absolutely NOTHING to do with the "Pixels" indicated on the page rulers when you set the ruler units to "Pixels," unless you deliberately set up that correspondence.
(I can't decipher from Jacob's tongue-in-cheek response to whom he is referring as "some." If "some" includes me, I assure you I am not saying this to confuse anyone. I'm saying this to help clear up the confusion that chronically occurs among newcomers due to this regretful element of the interface.)
Suppose for example, you have an image that you know contains one pixel. You import this image into an Illustrator document. The rulers are set to Inches. In the Transform palette, you set the height and width of this raster image object to 1 inch. You carefully position the upper left corner of the image to the page origin.
Based on what you observe by looking at the rulers, the resolution of this image is one Pixel Per Inch. Makes sense, right?
Now change the rulers' Unit of Measure to "Pixels."
Based on what you observe by looking at the rulers, the resolution of this image is one Pixel Per 72 Pixels. Wha...? Umm... its resolution is 1/72 Pixels Per Pixel? Its resloution is .013888... Pixel Per Pixel? What kind of sense does this make?
See? Remember: In order to know the resolution of a raster image, you need two values: A COUNT and a MEASURE. What the heck does "Pixel Per Pixel" mean?
In Illustrator, it simply means Pixel Per Point (1/72 inch).
...and I can only keep one or the other, so how do I keep both?
Sure you can have both. Again, any number of pixels can be scaled to any size, to result in any PPI. But in Illustrator, the only way an 800-pixel image is going to have a PPI of 300 is if it is scaled to measure 2.666... inches. Simply select the 800 x 800 image, set the Unit of Measure to Inches, go to the Transform palette, turn on the proportional chain link, and set the width or height to 2.66.
But if you then change the Unit of Measure back to "Pixels", don't expect the rulers to indicate a "width" or "height" of 800 "Pixels." They will indicate 192 "Pixels", because 2.66... inches equals 192 Points.
My art board is 800x800px,...
No. As you should now understand, your Artboard is, in fact, 800 x 800 points, which is 11.111... inches. If you don't believe this, just change your Unit of Measure temporarily to Inches. The only way you will get an 800 x 800 pixel image corresponding to this Artboard is if you export it to a raster image format (i.e.; create a raster image of it) at a resolution of 72 PPI.
I've set my doc raster effects settings to 300dpi.
That simply means that the raster images that are created when you apply raster-based live Effects (Drop Shadows, Glows, Blurs, etc.) will be created with pixels which measure 1/300th of an inch, according to Illustrator's rulers which, again, always refer to an actual unit of measure. So if your rulers are set to Inches, a 1 inch by 1 inch Effect will be rasterized to 300 x 300 pixels. If you change your rulers to "Pixels", the Effect will still be rasterized to 300 x 300 pixels, but your ruler will indicate that that raster image only measures 72 x 72 "Pixels." What that really means is merely that the image measures 72 points, which is equal to 1 inch.
Don't blame me. I didn't design the program.
(I can't decipher from Jacob's tongue-in-cheek response to whom he is referring as "some."
I am referring to the ones (none of whom is/are likely to post in this thread) that decided to:
A) Use the term DPI/dpi for PPI;
B) Use the term pixel for point.
I believe the 800x800px Artboard is simply what is set up in a document that has File>Document Setup>Artboard>Units set to Pixels.