There are multiple ways to achieve this behavior.

1. Use Blog Posts (Online Store -> Blog Posts), and make sure the article has the same handle as the corresponding collection, then get article content inside the collection template like this (we're using "news" as the blog title in this example):

{% for article in blogs["news"].articles %}
  {% if article.handle contains collection.handle %}
    {{ article.content }}
  {% endif %}
{% endfor %}

2. Use Pages (Online Store -> Pages), and make sure the page has the same handle as the corresponding collection, then get the page content inside the collection template like this:

{{ pages[collection.handle].content }}

3. Use collection descriptions. In Products -> Collections you can add your content in the description field, and access it in collections like this:

{{ collection.description }}

According to Shopify schema, a page is something with the url as follow - //mystorelink.com/pages/page-handle . So when you use {{ page.title }} it will display the page title only when the url is in the above format.

Don't confuse between a "Shopify page" and a "webpage" for both are completely different.

A Shopify page is a template while a webpage is a normal html page. In order for your requirement refer to following link types and templates

1. / or //myshoplink.com -> index.liquid -> {{ page_title }} & {{ page_description }}
2. /collections/xyz -> collection.liquid -> {{ collection.title }} & {{ collection.description }}
3. /products/xyz or /collections/abc/products/xyz -> product.liquid -> {{ product.title }} & {{ product.description }}
4. /pages/xyz -> page.liquid -> {{ page.title }} & {{ page.description }}

etc similarly for other templates.

P.S. You can have multiple product/collection/pages etc. templates using suffix values, but {{ <template>.title }} remains the same

P.P.S. If nothing is to be changed you can plainly use {{ page_title }} and {{ page_description }} everywhere. It defaults to the template currently in use.