To access specific collection attributes, you must know collection handle and use this kind of code :

{{ collections['the-handle'].url }}

So to achieve what you want to do, here is what you could do:

{% assign collection_handle = 'the-handle-of-collection-you-want' %}
{% for product in collections[collection_handle].products %}
    Do your stuff
{% endfor %}

Note that you cannot access a collection through its title. Only handle.

Learning more about what's handle: https://help.shopify.com/themes/liquid/basics/handle

HTH

For detailed information you may refer to Shopify documentation on Creating Alternate Templates or a similar blog post on Partners Blog.

These articles suggest creating files with particular collection handle, that can be selected manually. Since you do not want to do that and have specified that only filters change based on different collections, so instead of replacing the whole template you can simply include the different snippet or section based on collection handle.

Example, inside collection.liquid

{% if collection.handle == 'collection-1' %}
  {% section 'collection-filters-1' %}
{% elsif collection.handle == 'collection-2' %}
  {% section 'collection-filters-2' %}
{% else %}
  {% section 'collection-filters-default' %}
{% endif %}