Can someone please explain to me the difference between Owner Draw and Owner Equity?

"So it would be correct to use the draw account for a few random personal transactions?"

As long the tax entity type for the Business is Sole Proprietorship or Single-member LLC treated as SP, then yes.

"Is it okay to use the draw account for an electronic transfer to my personal bank account?"

You are asking two things, here:

The HOW it moved = electronic.

The WHY you took funds = draw

As for "Owner Equity", open the chart of accounts and try to open each Equity account. The one that does NOT have a Register view, no matter what it is named, is Retained Earnings, or Owner Equity that QB sill "close" the prior year into.

You cannot set up Subaccounts here.

I like NOT to see "Retained Earnings" but name that one Owner Equity.

Then, name the others for Draws (out) and Contributions (in).

At year end, you see Total Out and Total In. For Jan 1, close draws and contributions against each other and post the difference into Owner Equity. Now draws and contributions start at 0 for the new year.

"This article discusses another option...(quoting) If you pay for company purchases or assets with a personal check, credit card, or cash, you have, in effect, made a “loan” to your company."

There is no such thing as Loan To/From yourself, for a Sole Proprietorship.

For SP, we take Draws any time we want to. Or, we "reimburse" ourselves right away; you paid cash for Printer paper, and then write a business check to yourself for Office Supplies, to "buy" from yourself.

There is no Loan and no Liability account for this Tax Entity type.

The article linked is not the one I think you intended. 

Any reason not to just use use a single equity account for both money and and money out?

I would like to know the answer as well. One client's account uses Shareholder's distributions for money taken out and put in- same account. This is for S-Corp. Wondering how to set it up for single-person owned LLC