They are completely independent passwords and logins.
I’m confused by your wording that you ‘downloaded the app’.
Your topic is posted in the Sketchup Free category, which runs in your browser. To login in to that, go to app.sketchup.com, and login there with the email and password you used to register a Trimble account.
On the other hand, if you did indeed download Sketchup for desktop, start that program. Assuming it was the latest Pro version trial, you log in via the icon top right of the main Sketchup window, which looks like this: .
Login by clicking on it and choose Sign In.
Then enter your sign in email and password. When you have successfully signed in the icon changes to show a green tick, like this:
There’s no connection between the two. Log in either to the Web app, or from the Desktop program, as I described above.