Site content shows different from WP site that when using browser directly

Hi,
I would like to ask for help to explain/solve the following phenomena:
Everything I do in WordPress, write, create, change etc. and update… when checking result via “visit site” from WP menu, shows accurately on my site, so no problem there. But to
my chagrin I discovered that when I TYPE my domain name, which is obviously identical in a browser (I use Safari and Firefox) I see (but not always) not identical content. I could not believe it. Identical domain shows different content. So for example, some changes do not show as being updated, when looking at site via “Visit site” from WP, all was perfectly changed. In a menu, there are subcategories shown that I have deleted while ago and thus do not exist in my WP any more. When I click on such a subcategory, it shows error, article could not be found (of course not, it has been placed under newly created category because this one actually doesn’t exist…) So how could it survived still here showing itself to public when I removed it??) All this is beyond my understanding and to be honest, drives me crazy. Please, if anyone knows what I am talking about, or knows explanation, solution, please, share it with me. I lost so much time on this, I called server, hosting co. and called Internet provider, to flush cache (this was suggestion of server people) I spent whole day just on cleaning things, you name it, no change… The irony of it is, that sometimes browser shows it accurately. When that happen I thought; oh, finally it got fixed. But if I try few minutes later, there you go…. same problem. How can i know now what public could see. I spend time to do something and something else shows publicly.
Thank you so much for your time and I wait anxiously for the “genius” that would
figure this out…
My warmest regards, Maya