To add to the many helpful comments thus far. I would like to point out that the question,
"I would like to know how matte paper or glossy paper react to ink on press".
Can be a complex question depending on who you ask.
The reactions on press will change in accordance with each stock's unique characteristics. As pointed out by others, the superior surface efficiency and reflectivity on gloss coated stocks, typically result in a greater possible D-Max(density maximum), both for 4-color inks and spot-color inks when compared with what's commonly possible with matte coated stocks. Increasing the D-Max accompanies with it an increasing color gamut as well, provided the press is well run and maintained.
Another factor is the absorbency, or "hold-out" of the stock. For example, "cast coated" papers exhibit both high gloss and high absorbency characteristics. Whereas "super calendared", #1 premium gloss coated stocks exhibit high gloss but with much less absorbency(better hold-out) than cast coated stocks. More absorbent stocks "dry-back" more so than do less absorbent stocks, and therefore change the appearance of the sheet as it dries, more so than less absorbent stocks do. I do not mean to favor one coating over another, just to point out differences.
Another item to consider is that the higher the surface efficiency of a stock, the lower the amount of "squeeze" the pressman needs to apply to the stock in order to achieve uniform ink transfer to the stock. In other words, matte coated stocks typically require somewhat more squeeze than gloss coated stocks require due to their less uniform matte surface. More squeeze oftentimes results in more sheet fan-out, dot-gain and other negatives with respect to a job as was pointed out earlier.
Don't forget the "brightness" and "whiteness" of each stock, a cool-white gloss stock might show significant hue and gray balance shifts when compared to a warm-white matte coated stock.
The UCR/GCR settings might react with substantial differences on matte stocks when compared to gloss stocks and should be considered.
Lastly, there may also be noteworthy differences in the way varnishes and coatings adhere and behave between gloss coated and matte coated stocks.
As a general rule of thumb, gloss coated stocks will result in both higher quality results and less trouble on press, but not always. A great matte coated stock might trump a "dirty-low-down" gloss coated stock on a good day.
"Does matte absorb the color more into the paper thus making prints darker than glossy or is it the other way around?"
Typically gloss coated prints have a greater D-max and therefore can achieve darker shadows than matte coated prints. Absorbency has been discussed already as well.
I suspect that what you actually meant by "darker" was not D-Max, but rather the loss of dynamic range and all the accompanying detriments incurred alongside the diminution of surface efficiency from gloss stocks to unbleached newsprint. I think Gordo said it best,
If tonal compensation has not been applied in the form of a plate curve or through separation techniques then there may also be a further loss in midtone and shadow detail and tonality.