This is a question about the phrase "botella de agua". How does one make the distinction between a bottle filled with water and a bottle normally used for the purpose of carrying water? For example, in English one might say, "Each person should fill their water bottle before we leave." Or, "Please pass me that bottle of water."
A "water bottle" may be filled or unfilled. A "bottle of water" would definitely be filled with water regardless of whether it's a water bottle or not. For example, a wine bottle filled with water could be called a "bottle of water" but not a "water bottle". Likewise, one could call a filled-up "water bottle" a "bottle of water", but one wouldn't say "Please pass me that bottle of water." referring to an unfilled "water bottle".
This distinction applies to other phrases too, especially when an object can contain something. For example, asking someone if they would like a "tea cup" is quite different than asking if they would like a "cup of tea". But both would be called "taza de té" in Spanish? Pencil box vs. Box of pencils. Pig pen vs. Pen of pigs. Wood shed vs. Shed of wood or wooden shed. Etc.