As per Guide - Product Backlog refinement is the act of adding detail, estimates, and order to items in the Product Backlog.

If that's how your team is choosing to perform their estimates. The Scrum Guide does not prescribe how the team should estimate or how granular the estimates should be (story level vs task level). 

When we say 'Estimate' does it includes estimation of 'Sub-Tasks'? (E.g. Development task, Testing tasks etc in Hours) or Story in story points ?

Agree with @Tony , there is no specific rule and neither its in Guide. What does your development has to say on this ? Are they able to plan their work for a Sprint ? 

When we say 'Estimate' does it includes estimation of 'Sub-Tasks'? (E.g. Development task, Testing tasks etc in Hours) or Story in story points ?

It all depends on what your team deems suitable. If you think estimating on subtask level is improving your transparency or ability to deliver a done increment which suits the Sprint Goal, sure!

we estimate the story in story points during the Sprint Planning

I would advice the stories to be estimated during refinement sessions and not Sprint Planning event.

This will also help your team and PO to craft a Sprint Goal and forecast during the Planning event

Also user stories are not necessarily the best format, but it's about the 3 C's idea behind it:

- Card (user story, task, sub-task, banana peel). The card contains an idea, with limited information. This way the  development team doesn't get biased on how to do the work and keep a creative, open mind.

- Conversation: Development team has a conversation with P.O. (or stakeholders, if necessary) to understand and add details.

- Confirmation: Through for example acceptance testing, the details and outcome are verified.

More info:

L-l-l-linkie!