Basic Income and Negative Income Tax are an in fact equivalent, in that you can achieve identical income functions with either just by choosing the right tax bands.

However, their framing leads to different expectations. For example consider a flat income tax of 25% on income less $20k (going negative below that so unemployed people get $5k credit). Raising the negative rate to 50% sounds kind of progressive, since you're giving more to poorer people, but frame it as Basic Income, and yes you're increasing the baseline from $5k to $10k, but you're also implementing a 50% regressive tax band up to $20k earned income.

Another point is that they'll tend to be implemented differently due to framing. Basic Income is likely to be part of the welfare system, and since it's unconditional, you can just register once and receive it in perpetuity. Negative Income Tax is likely part of the tax system, so to get it you potentially need to submit a tax return saying "Earnings: $0" every year, which makes it more embarrassing.

It still requires a level of means testing. People might hide sources of income in order to get more payments. On the other hand, since you aren't handing a check in the same amount to every person in the country, it wouldn't require as high an income tax rate to sustain.

I support a prorated version, but the common criticism is that it's more open to fraud and harder to implement. I still think a prorated[1], guaranteed minimum income is better than a basic income.

1) something like reducing that payment by $0.50 per $1 earned as an example.

It's just an unnecessary wrinkle. Taxing earned income is the same as doing what you propose, but incurs higher coordination costs. Also, using your example, it's regressive taxation unless the base rate is higher than 50%.

I don't think paying everyone is a good idea and will encourage inflation to make the program useless. I'm fine with regressive when talking money given to you.