In kB or pixels?
If the former, the kB sizes depend on the quality (JPEG)/number of colours (GIF).
If the latter, please specify the actual pixel sizes, and preferably the nature of the vector artwork, and the time of sunset.
Why when saving/exporting to gif, the image is smaller than saving/exporting to jpg?
The fewer colors, the more efficient. That's why. JPEGs always compress truecolor and thus even a simple b/w image is "inflated", if you will. GIFs on the other hand only store the actual colors used up to 256 colors. Even the dimensions don't matter much in that case. You can get very large GIFs to result in very small file sitzes if they do not contain that many discrete colors.
Pixels. It looks like it's actually increasing in pixels when exported as a jpg and remaining the same size dimensionally when saving as gif. As a gif, it's aprox. 350 x 200 pixels, as jpg it increases to 1600 x1200 approximately.
Bit/Byte size of file:
gif = 233 kB
jpg = 4.7 kB
The jpg is saved at 10, high quality.
The JPEG size seems to reflect the resolution setting at Export.
Why when saving/exporting to gif, the image is smaller than saving/exporting to jpg? (not currently in program to have specifics of save vs export, if it matters)
Not always... sometimes the jpg file is smaller... a lot depends on the content. Anyway, don't worry about that, it's not important. What is important is when to use jpg and when to use gif. Below is a rule of thumb.
When to use use jpg:
1/ When you have an image (photo)
2/ When you have raster effects, eg: gradients, drop shadows, etc.
When to use gif:
1/ When you have flat colours
2/ When you need a transparent background (the importance of this. for your particular need, could overrule jpg 1/ above)
Then there's png:
Advantages of both, but typically larger file sizes
Please remember, that all the above are 'lossy' formats. Meaning, they discard image information. Resaving each will result in progressively degraded images. IOW, a jpg'gif saved as a jpg/gif is worse in quality than the original jpg/gif.
Keep masters in the native format or as TIFF (.tif)
Since it's clear you're talking about an actual difference in pixel dimensions, I think Jacob has a handle on the possible cause.
Try using Save for Web (& Devices) instead of a straight export. Pay attention to the pixel dimensions in the image size panel within the SFW dialog. If that's the same for both your JPEG and GIF saves, the results should be consistent.
So if I want a high resolution (just to have the best image possible) there is no way to constrain/set the image size? This may be pretty basic, but why would anyone want the image pixel/dimensional size to increase more than what it was designed at/for, because of a resolution setting selected when exporting/saving?