As has already been stated, anti-perspirant is designed to reduce or totally prevent sweating in the areas where applied, and deodorant is designed to mask unwanted odour(s). I subscribe to the belief that artificially interfering with bodily functions on a systematic and habitual basis is to take signifacant risks. Deodorant only covers up anything untoward but does not eliminate it - rather like air fresheners only overpower general smells in the same way noise drowns out speech. To my way of thinking, it is by far best to reduce or eliminate the causes of unwanted smells. This is not always possible, but knowing the source is essential. In the case of odours generated by sweat on the skin, it is caused by micro-organisms digesting the substances contained in our sweat (pure virgin sweat is odourless). As they do so they multiply and give off wastes. Reduce or remove the fauna and you will reduce or remove the odours. Obviously, washing is important but since (I think this is correct) a lot of the fauna consists of yeasts, they are killed by vinegar, a totally natural product. After washing (and well after shaving underarms, if you do) wet a bit of cotton wool in vinegar and rub over skin. Leave vinegar on and (if you wish) wash off after some hours (perhaps overnight). Do this regularly and I would expect you not to need either deodorant or anti-perspirant, although this does depend a bit on your personal characteristics, including how heavily dressed you need to be to feel comfortable indoors (i.e. heating levels - the colder the house, the thicker the jumper and the more the underarm sweat - even more important to wash self and clothes frequently).