No, that's not quite how it works. A semi trailer puts a portion of its weight, loaded or not, on the tow vehicle. That's the whole reason its named "semi trailer".
A pull trailer supports its own weight, and load, so it doesn't need a jack on the tongue. Okay, con gears (used to convert semi trailers to pull trailers do have jacks since they're heavy).
Below are two examples of typical semi trailers.
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And here is an example of two pull trailers. Unusual ones, but pull trailers nevertheless, with steering front axles.
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Come to think of it, the really simple way to tell a semi trailer from a pull trailer is if it has a steerable front axle or not. If it doesn't, it's a semi trailer.