"in UK" and "in the UK" what is the differences
between this two useage?
'In the UK' is the more correct form.
'UK' stands for 'United Kingdom', which needs an article i.e. The United Kingdom. Likewise, you should say 'to the UK', 'from the UK' and so on.
That said, you will occasionally hear some expatriate British people use the form without the article. I would avoid this if I were you. If a foreign learner were to use this form it would simply sound like a mistake. You should stick with the form that you know is correct : 'In the UK'.
"in the UK" - if you are referring to the country ("the United Kingdom of Great Britain and Northern Ireland") is correct. "I am from the UK" but not "I am from UK".
You can say "there are a many fine buildings in UK cities" or " many UK citizens live and work in France" where you are using "UK" as an adjective describing a noun ("cities, citizens")