TENSE refers to the absolute location of an event or action in time, either the present or the past. It is marked by an inflection of the verb:
David walks to school (present tense)
David walked to school (past tense)
Reference to other times -- the future, for instance -- can be made in a number of ways, by using the modal auxiliary will, or the semi-auxiliary be going to:
David will walk to school tomorrow
David is going to walk to school tomorrow.
Since the expression of future time does not involve any inflecton of the verb, we do not refer to a "future tense". Strictly speaking, there are only two tenses in English: present and past.
ASPECT refers to how an event or action is to be viewed with respect to time, rather than to its actual location in time. We can illustrate this using the following examples:
[1] David fell in love on his eighteenth birthday
[2] David has fallen in love
[3] David is falling in love
In [1], the verb fell tells us that David fell in love in the past, and specifically on his eighteenth birthday. This is a simple past tense verb.
In [2] also, the action took place in the past, but it is implied that it took place quite recently. Furthermore, it is implied that is still relevant at the time of speaking -- David has fallen in love, and that's why he's behaving strangely. It is worth noting that we cannot say *David has fallen in love on his eighteenth birthday. The auxiliary has here encodes what is known as PERFECTIVE ASPECT, and the auxiliary itself is known as the PERFECTIVE AUXILIARY.
In [3], the action of falling in love is still in progress -- David is falling in love at the time of speaking. For this reason, we call it PROGRESSIVE ASPECT, and the auxiliary is called the PROGRESSIVE AUXILIARY.
Aspect always includes tense. In [2] and [3] above, the aspectual auxiliaries are in the present tense, but they could also be in the past tense:
David had fallen in love -- Perfective Aspect, Past Tense
David was falling in love -- Progressive Aspect, Past Tense
The perfective auxiliary is always followed by a main verb in the -ed form, while the progressive auxiliary is followed by a main verb in the -ing form. We exemplify these points in the table below:
