Red switches are linear switches. They have no tactile bumps, and therefore there is no change in key feel until you hit the bottom of the key. Linear switches are said to be quieter than other switches (Tactile or clicky), but they still make a lot of noise if you press the keys hard.
Brown switches are tactile switches. They have a tactile bump that you can feel as you press past the bump on the slider, giving you a tactile feedback.
Blue switches are clicky switches. They have a mechanism inside the switch that creates a clicking noise. As a result, they are the loudest out of three.
If you want a mechanical keyboard that's quiet for office and such, these ones probably aren't what you are looking for. I personally recommend switches that have silicone dampeners in them (like Cherry MX Silent Red, Black, and more) or a decent membrane keyboard instead.
These switches are referred to as "Low Profile" switches. In terms of the height, while they are considerably shorter than the "full-size switches", compare to other low profile switches (say Kailh Choc), they are fairly tall.
Here is a review of the keyboard that goes into details about what the keyboard is like.
good keyboard, they also have the non-TKL one on special (I use brown switch one and love it)