"Is it not possible to get search results on another page then the archive page for that cpt?"
They are separate things. There is an archive for a custom post type (e.g. site.com/project/ would display the archive of the Projects post type). And there is the search archive, a special WordPress archive to show results from a standard WordPress search, (normally) invoked by the 's' URL parameter, e.g. site.com/?s=chevrolet.
You can customise the standard search archive (as we have been discussing above), including customising which post types are included in the results. There is only one WordPress search archive, so a custom search archive would affect all such searches.
A theme would typically include a search box in the header or main navigation which uses this standard search archive.
Now, you can create a custom search with Views which has nothing to do with archives, and specifically the search archive, and I think this is what you want.
So, go to Toolset > Views and create a View for the post type in question (glossaries), specifying that this will be a custom search View.
In the Search and Pagination section insert a text search control and a submit button.
Then design the output much like I think you already did when you were experimenting with archives.
Now go to the page where you want this search to appear and insert the View directly in the page (using the Fields and Views button).
Visit this page on the front end and you should see a text search input where users can enter their search terms.
Note that this would normally search the title and post content of the glossary posts. If you have content in custom fields that you want included in the search, you would need to add the Relevanssi plugin and set it up according to https://toolset.com/documentation/user-guides/searching-texts-custom-fields-views-relevanssi/.
Any outstanding questions, please ask away.