Is it possible to have trade deficits WITHOUT having a budget deficit?

I would think that the two phenomena are *NOT* related at all. Trade
deficits occur when you import more than you export. The USA happens
to import close to a trillion dollars a year. Incidentally, we run a
deficit slightly lower than this.

Most people can easily understand a budget deficit, and the
ramifications of a budget deficit.

However, a trade deficit - which I can easily understand - seems to be
equated with a lavish lifestyle, running up deficits, and an economy
unable to save.

Here are my questions:
1. How and why do people correlate a trade deficit with a low savings
rate?
2. Is the savings rate at the consumer level or at the governmental
level?
3. Finally, here's a hypothetical scenario - please tell me what you
think: The USA imports $1B in goods/services from a country, and that
country imports $1B from the USA as well. There is neither a surplus/
deficit with this country for either parties. The USA, however,
imports a goods/services that the exporting country has no profits.
Their net profits in doing business is 0%. However, the USA is
selling something very lucrative to this nation, and the shareholders
have made $100M from the exporting of $1B (10% profit margins).

On paper, both countries have the same trade deficit/surplus. But the
Americans are in a much better predicament. Please clarify if my
assessment is correct - that the USA is benefitting more from this
trade relationship?
.

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