Hi @SHUMAN and welcome to the Community!

Every sign up form can be configured to collect details like email, phone number/SMS, name, etc. In that sense, a signup form is typically synonymous with “user registration form”. 

One way to accomplish the sharable URL form that you mentioned would be to embed a full subscribe page on your site. Once you’ve created a List to house your subscribers within Klaviyo (Audience > Lists & Segments > Create List / Segment > List > Name and Create), click on the list and navigate to the Subscribe & Preference Pages tab from the header navigation menu. Here, you can customize the styling of your subscribe page and add custom fields:

Once you’re done customization the page to your liking, you can embed it in your store using the instructions in this Help Center Article:

https://help.klaviyo.com/hc/en-us/articles/115005251988-Embed-a-Full-Subscribe-Page-on-Your-Website

Once you’ve embedded the page, you can share and forward its URL and customers will be directed to a single page dedicated to sign up.

In response to your second point, it’s not currently possible to embed a sign up form in an email template. This is because inbox providers may recognize sign up elements as security risks which could harm sender reputation.

For more context on this, check out these Community threads regarding the same issue:

Hope this helps and thanks for using the Community!

- Brian