Adobe Illustrator Colors differ from 'in web colors'

Hi together! I started using the Adobe tools some months ago and I am still learning. So, please be patient with me :-) I designed a logo in AI, using 3 colors (RGB): #6699CC #333366 #663333 However, when switching to the website, these hex codes are not showing the same colors on the web. The same thing vice versa: If I use the hex codes from the web, they look different in AI. I already found out that ... a) hex codes are not unique and b) that there's this 'in web color', which is the nearest... errr... kind of fix color in AI. And I already know that I can assign a certain profile (although as a beginner, I am a bit overwhelmed by this choice). However, it did not change the result: The 'in web color' is always different to my original one, no matter which profile I am choosing. On my website, I simply helped myself by using a color picker and getting the web-based hex codes. Works fine. However, as there is a hex code on the web which is related to exactly my color, I don't get why the same is not available in Illustrator. But I worry what will happen when I'll create the printable stuff, using the CYMYK model. Will the printed result look like my original color or like these 'in web colors'? Up to now, I found nothing which helped me understanding if it's a problem not to use the web colors and how to get rid of that and keep my original colors. So, I appreciate all hints and solutions which are easy to understand by not-yet--experts. If there's a good tutorial which helps me understanding, I'll also be happy with it. Thank you in advance and have a great day! Katrin