"Modality in English verbs refers to auxiliary verbs that express how the action is looked upon by the speaker. Modal auxiliary verbs cannot act alone in a sentence; they are “helping” verbs only. The ten modal auxiliary verbs are: can, could,may, might,must,ought to,shall,should,will, and would" (source).
"Tense refers to the location of an event or action in time" (source) Following is an overview of tense in the English language.
Present: action that occurs now; routine actions - The children play outside every afternoon.
Past: action that occurred at a specific point in the past - She organized a surprise party for her brother.
Future: action that will happen at some point in the future - He promised he will have his homework done before he leaves the house.
Present perfect: "action that began in the past and continues to the present" (source) -I have given you enough chances to clean your room.
Past perfect: action that completed in the past before another action in the past began - If only he had left his apartment on time, he would have missed the intruder.
Future perfect: action that "will be completed before another takes place in the future" (source) - They will have graduated by the time you arrive.
Present progressive: action currently in progress - The baby is sleeping.
Past progressive: action that continued for a period of time in the past - I was working for a travel agency when I was in college.
Future progressive: continuous future action - My mother will be taking her grandchildren to Disney World.
Present perfect progressive: action that began in the past but continues in the present - He has been playing soccer since early this morning.
Past perfect progressive: action that was in progress before another action in the past - She had been studying so long she forgot to eat dinner.
Future perfect progressive: action that will happen for a period of time at a specific moment in the future - Her uncle will have been singing opera for 20 years by his next birthday.
"Aspect refers to how an action is to be viewed with respect to time, rather than to its actual location in time." (For more information, see http://www.ucl.ac.uk/internet-grammar/verbs/tense.htm). This is accomplished through the use of adverbial phrases or the inclusion of auxiliary verbs. For example:
Noah purchased the winning lottery ticket while he was on vacation.
Noah has purchased the winning lottery ticket.
Noah was purchasing a lottery ticket before he realized he’d forgotten his wallet.