When you click on the 'Tags' button inside a contacts record this is where you can select the tag via the checkboxes as shown in the example below: 

If you do not see some of your tags that you know you have set up this is likely to be because some of your tags are not set up as global tags - hence you will not see them in the checkbox list of tags - they are set up as 'ad-hoc' tags.

The ad-hoc tag (if applied to a specific contacts record) will be shown inside the free text area as shown in the example below the ad-hoc tag is called 'april-18'. 

If tags have been setup as 'ad-hoc' tags where someone has either imported these contacts with these tags (without having set them up inside the Global Settings page or added them in the tags box free text area as a 'ad-hoc' tag (please see the example above) these tags will not be displayed inside the Edit Tags window where the global tags are shown with checkboxes, please see image 1.  

To explain the difference further between global tags and ad-hoc tags please see the link below:

What is the difference between a global tag and an adhoc tag?

In this case it would be best to make the ad-hoc tags global tags so that you can then see them when you click on the 'Tags' icon inside a contacts record. 

If you have any questions please contact our Support Helpdesk.