What is the real difference between themes?

Are themes really ‘specially designed’ for different purposes, or are they primarily different only in fonts and colors? I could really use some help sorting this out. I want to set up a site with the following features and would so..so..so.. appreciate any recommendations you might have:

1) Blog – probably the home page, but want static page option.

2) Variable layouts – sidebars and full-page widgets available and assignable to individual pages.

3) Courses (I see you have a plugin for this)

2) Display of Courses – with clickable grid-type display to go to the course – and notification if course is available only to members.

3) Membership – three levels a) everything on site available, b) selective courses and selective pages available, c) prospects or non-members see partial content – ‘more’ shortcode to offer to sign up

d) visitors – limit content visibility, but have teaser visibility

4) Membership payable monthly or annually .

5) Ability to drip content and /or emails to members and prospects.

I am perfectly happy if Paypal is the only payment option – at least for now.

And of course it must be responsive.

I just read this and realize it sounds like I’m asking you to do all the work….I really just need an explanation of what the real difference is between themes, and are some better suited for some reason than others, based on my needs? I’ve used ithemes, and developed sites before, so I’m not completely inexperienced… just not sure how YOU do it.

Sorry to be a pain, but I’d like to get started, and I’m not sure where to start.

THANK YOU THANK YOU THANK YOU for your response.