Learn English – something full of/ a full something of

In the pure sense of your words, differences do exist.

1. a bowl full of mush

2. a full bowl of mush

3. a bowlful of mush

The comments have yielded a third option, "bowlful", which is by definition a means of quantifying just how much. For instance, a cupful of flour can be added to a recipe or dumped onto a pastry slab and remain a cupful, despite the fact that it is no longer in a cup.

"A bowl full of mush" is like "a cup full of flour", in that its contents can be emptied and it will remain "a bowl" but no longer be a "bowl full ...". Thus this structure describes a thing that happens to be full of something else. It is more interested in describing the thing than it is in quantifying the contents of that thing. Put another way, a cup full of flour is not added to a recipe, because the cup would be inedible.

"A full bowl of mush" places greater emphasis on the fact that the bowl is full, and as such it does indeed quantify, but not quite in the same manner or to the same end as a bowlful. Its contents, either when emptied or consumed, will not remain "a full bowl".

Consider the following sentences:

Little Bobby ate a full bowl of mush this morning.

Little Bobby ate a bowlful of mush this morning.

What is in little Bobby's stomach is a bowlful of mush, but not a full bowl of mush, which is something that a boy could not possibly swallow. In the first sentence, someone (let's say Bobby's mother) is emphasizing just how much the boy ate, perhaps more than he typically has on past occasions. In the second sentence, by contrast, someone is merely stating the quantity that the boy ate, as opposed to emphasizing that quantity. The bowlful is nothing exceptional but should be sufficient to stave off the boy's hunger.

Perhaps a useful example would be "a tankful of gas/petrol" compared with "a tank full of gas/petrol" and "a full tank of gas/petrol".

The first choice clearly expresses a quantity of fuel that, even should the fuel be consumed, remains the same quantity. For example, it might take three tankfuls of gas/petrol to drive from point A to point B. Even after the fuel has been consumed, the statement of quantity remains true. A 'day's march' is a day's march (x miles) whether you've done it or not.

However, "a tank full of gas/petrol" would serve as an accurate description of a fuel reservoir (provided that it is full) below ground at a station, in transport from refinery to station, or installed behind a building to provide fuel for heating, power generation, etc. Once this fuel is consumed, we are left with an empty tank (i.e., the original statement is no longer true).

"A full tank of gas/petrol" once again places emphasis on the fact that the tank is full. In usage, this statement is much more likely to apply to a precondition for travel, transport, and so on. As in the second option, once this fuel has been consumed, we are left with an empty tank and the original statement is no longer true; however, the third construction is not necessarily interchangeable with the second.

In the imaginary news report "Three people died today when a ______ of gas/petrol exploded", it would be natural to favor the second construction, "a tank full". It would thus seem that both "a full tank" and "a full bowl" are used in a more personal manner, with emphasis placed according to the opinion of the speaker that this quantity is of utmost importance, than are "a tank full" and "a bowl full", with the quantity expressed in a way that is less emphatic and therefore less subject to personal opinion, a mere reportage of fact.