Despite being a pejorative, confusing term, the word senile has a fairly straightforward meaning: the state of being aged. Biologists make a distinction between senility and senescence, the progressive lowering of biologic efficiency and capacity of the organism to maintain itself efficiently. Medical dictionaries commonly describe a senile person as experiencing the mental and physical deterioration characteristic of old age, or the cognitive and physiologic signs of advancing age. Although the definition doesn't imply the person has dementia, the word senile is commonly misused to imply someone does have dementia.
The medical community itself has contributed to the misconception that being called senile implies being demented: beginning in the 1960's with the 2nd revision of the Diagnostic and Statistical Manual of Mental Disorders (DSM), published by the American Psychiatric Association to provide a common language and standard criteria for the classification of mental disorders, the term Senile Dementia of the Alzheimer's Type was used to characterize people age 65 and older who were suffering from Alzheimer's disease. The term pre-senile dementia referred to a person who developed dementia before age 65. It wasn't until the 4th revision of the DSM in 1994 that the terms senile and pre-senile were removed from the manual: now, a person may have Dementia of the Alzheimer's Type with Early Onset or with Late Onset.
In classic literature, it's not hard to find references to senility that paint an unflattering picture. Consider the following passage from Jack London's dystopian novel The Iron Heel, first published in 1908 (one year after Alois Alzheimer published his original case report describing the first known case of Alzheimer's disease):
The stream moved slowly, while from it arose groans and lamentations, cursings, babblings of senility, hysteria, and insanity; for these were the very young and the very old, the feeble and the sick, the helpless and the hopeless, all the wreckage of the ghetto.
Because so many words describing elders are negative and pejorative (geezer, decrepit, codger, biddy, fogy), it is probably best to avoid using the term senile when describing someone who is aging. The distinction between forgetfulness and Alzheimer's is a much more meaningful way to understand the difference between normal aging and dementia.
Adams, Raymond D., Victor, Maurice, Principles of Neurology, Third Edition, McGraw Hill Book Company, 1985, p.450
London, Jack, The Iron Heel, Mondial Books, 2006, p.168