Extensions of all types are returned.
Only search tools are returned
When performing a search from the search tools page 1 the issue in not reproducing, the result list contains all types of extensions.
Verified in FF 60.0.1 on Win7(x64) Issue can be reproduced on amo-dev, amo-stage and amo-prod
Screencast for this issue:

cc @willdurand as I think this may be a frontend-thing. From what I can tell once you click on the "next page" button you're leaving the /search-tools/ page and enter the regular search. I don't think that should happen.
I guess it is a frontend issue, investigating...
From what I can tell once you click on the "next page" button you're leaving the /search-tools/ page and enter the regular search.
So, I believe that is intended (but I was not there when this was decided). My understanding is that /search-tools/ is a landing page and we have to go to the search page for more results.
See also: https://github.com/mozilla/addons-frontend/issues/4496
Interesting, that's a bit confusing but then "working as expected" I think. The results do what the user expects though, mostly, so this shouldn't be much of a problem.
Thanks for investigating! Closing.
I do not think this should be considered as expected because the current behavior is counter intuitive.
When searching from the landing page (/search-tool/ )all types of add-ons are returned and when searching from the page 2 (/search/) only search tools are returned.
The request that is made when performing a search from the landing page looks like this: https://addons.allizom.org/api/v3/addons/search/?app=firefox&appversion=60.0&platform=windows&q=fire&lang=en-US&wrap_outgoing_links=true
And when searching from page 2 looks like this: https://addons.allizom.org/api/v3/addons/search/?app=firefox&appversion=60.0&platform=windows&q=fire&sort=relevance&type=search&lang=en-US&wrap_outgoing_links=true
In the second request we have "type=search". Is that ok? If yes, why we do not do that in the landing page?
@willdurand @EnTeQuAk
The request that is made when performing a search from the landing page looks like this: addons.allizom.org/api/v3/addons/search/?app=firefox&appversion=60.0&platform=windows&q=fire&lang=en-US&wrap_outgoing_links=true
And when searching from page 2 looks like this: addons.allizom.org/api/v3/addons/search/?app=firefox&appversion=60.0&platform=windows&q=fire&sort=relevance&type=search&lang=en-US&wrap_outgoing_links=true
In the second request we have "type=search". Is that ok? If yes, why we do not do that in the landing page?
See the filters on the left, you will see that the "add-on type" is "search tools" when you navigate to page 2. That's why the search behaves differently.
When you access https://addons.allizom.org/en-US/firefox/search-tools/ the filter "add-on type" is set to Search Tool.

If you perform a search in there the request that is fired is this one:
https://addons.allizom.org/api/v3/addons/search/?app=firefox&appversion=60.0&platform=windows&q=fire&lang=en-US&wrap_outgoing_links=true
which does not contain "type=search" - extensions of all type are returned.
When you navigate to the second page https://addons.allizom.org/en-US/firefox/search/?page=2&sort=relevance&type=search the filter "add-on type" is set to Search Tool. If you perform a search in there the request that is fired is this one:
https://addons.allizom.org/api/v3/addons/search/?app=firefox&appversion=60.0&platform=windows&q=fire&sort=relevance&type=search&lang=en-US&wrap_outgoing_links=true
which does contain "type=search" - only search tools are returned.
ah right, sorry for that.. We should probably not display the filters on /search-tools/.
Reopening based on comment https://github.com/mozilla/addons-server/issues/8402#issuecomment-393556441
@madalincm could you reopen this issue on addons-frontend instead? thanks!
I have logged https://github.com/mozilla/addons-frontend/issues/5182
Closing this issue.
Thanks @willdurand