Rabbi Shimshon Refael Hirsch has a number of interesting writeups on the relationships between words and their meaning. This shabbos, our rabbi brought up the relationship between מלאך (Malach - Angel or messenger) and מלאכה (Melacha - work). This is the way that Hebrew connects words to the noun that applies to them. Consider the piyut on יום כפור, that starts הנה כחומר, as an example of seeing how the noun is created from the מפעיל, the causative usage.
In Parshas Vayera, the meforshim say that the reason that three מלאכים came to אברהם and only two continued on to סדום to save לוט was that a מלאך only exists for as long as its task (מלאכה) has not yet been accomplished. Once the job is done, the מלאך no longer exists. Similarly, we can connect the 39 מלאכות of שבת to the person doing them and to the definition as those things being done for the משכן. Similarly, the word מלאכה is used when speaking of the "work" that השם "did" creating the world. We see that this term is used for a task that is directly connected to the person doing the job.
This is opposed to the word עבודה which seems to be used for work that is imposed from without and is meant as "service". For example, a person who does עבודה is an עבד which is normally translated as "slave" or "servant". This means that instead of being something that is intrinsic to the being (מלאכה performed by a מלאך), this עבודה is an external task that is assigned by a "master". The being performing the עבודה is totally separate from the "work" being done. As a result, a מלאך cannot do עבודה as its "work" is intrinsic to its being. This means that animals, lacking free will, and created to work only according to the natural laws set up by השם can only do עבודה. A human being, created by השם, with both aspects of the universe, and with the free will to choose between them, can perform מלאכת or עבודה, . An example is seen in Parshas Bereishis (פרק 2: פסוק 15) where the purpose of אדם being in גן עדן is "לעבדה ולשמרה".