First and foremost, let me explain what WordPress is, WordPress is a (free) open source web application which powers over 40million websites. WordPress is a common application which developers choose to base customer websites on, this appears to be what has been done for you.
In order to make a WordPress install look unique for a client, WordPress has what it calls Themes (themes are basically the skin of the website). WordPress has a default theme, which appears to be what is activated currently on your website.
It appears (to me) that your webhoster may have had an issue of some kind, and as a result, WordPress has switched to the default theme instead of your theme, which is what has confused you.
In order to switch it back, you'll need to log in to your WordPress install, access the Appearance -> Themes menu (Varies depending on what version of WordPress is installed, if it's been neglected, it may be an older version), and activate the theme which looks like your original website.
To get your login details, you'd need to contact whoever originally set up the WordPress install for you, However, I can take a guess that your username is most likely the default 'admin' username, If you follow the login link, you'll come to a Password Reset screen, by entering 'admin' into that form, you should be emailed a link to change your password.
If for some reason, that doesn't send you an email, It may be that the Email address registered for your account from when it was set up, may have been directed to your previous web designer.
So, To be clear, WordPress hasn't forcably taken over your website, No-one in the WordPress team has access to your website, It's just the software which your developer chose to use.