Are deber and tener que interchangeable or are there differences in meaning and use betwen them.

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Accepted Answer

Hola Emanuel
Deber and tener que are generally interchangeable. However, tener que is normally used to express what someone has to do and whatever that is, is not totally dependable on the person but on "external factors"; Deber is also used to express what someone has to do but this obligation is more of a moral obligation and it depends on the person, not external factors. Here are two examples with a bit of context:

La estación de trenes está bastante lejos. Si quieres llegar a tiempo, tendrás que coger un taxi.
The train station is quite far. If you want to get there on time you will have to take a taxi.

Here I used "tendrás que" because there are external factors (the train station being far away).

Antonio, debes ser más generoso con tu hermano.
Antonio, you have to be more generous with your brother.

Here I used "debes" because it is more of a moral obligation and it is totally dependable on Antonio. 
We tend to use "tener que" a lot more than "deber" though. 
I hope this helps.
Inma

Answer

This is really a great explanation. Thank you.

Answer

"Deber + infinitive" vs. "tener que + infinitive"

"Deber + infinitive" tends to imply a sense of *internal* obligation, whereas "tener que + infinitive," which is extremely common and very close in meaning, tends to convey a sense of *external* obligation.

Emilio debe levantar su ropa sucia.
Emilio should pick up his dirty clothes. (For his own good and that of the household.)

Emilio tiene que levantar su ropa sucia.
Emilio must/has to pick up his dirty clothes. (Or his mother will ground him.)

I researched this because the question was: She had to serve coffe to the customers. That is hardly an internal or moral obligation but a conditioin of her employment imposed on her by externel factors; i.e her boss. Not a good example for using deber. Tener que would be more appropriate.