It is the same thing. Unless you are paid on a W-2, you are by default an Independent Contractor or non-employee. Because there were no taxes withheld, you are responsible for them. Then income is entered on Schedule C and the SE taxes are calculated on your profit.
I am not a sole proprietor and should not be responsible for anything but my IRS taxes due. I have not held a regular job in 2019 and my "employers" should have paid all payroll taxes. How can I enter this in Turbotax to reflect properly?
You have two options. You can file Schedule C for your non-employee compensation or File Form 8919.
Workers who believe an employer improperly classified them as independent contractors can use to figure and report the employee’s share of uncollected Social Security and Medicare taxes due on their compensation.
The reply by @ColeenD3 is correct. You are considered to be self-employed and are responsible for your employment taxes.