No - you have two separate elements: Your defence and your attack element (the same goes for monsters).
Your defence element is applied when you receive damage. It can have multiple levels - so you (and monsters) can be Water 2, or Fire 1, and so on. By default, you are Neutral 2, if you use an enchantment potion you become level 1 of that particular element. Think of it as a coat applied over your character, that determines how effective attacks against you are. Your defence element is determined by enchantment potions (temporarily) or special spirit bottles, such as Casper's (permanent, as long as you have the item equipped).
Your attack element is used when you deal melee damage. It has no levels - you either deal fire melee damage, or water melee damage, and so on. By default, your melee attacks are non-elemental, Neutral damage. Your attack element is determined by special weapons you wear on your main hand, such as fire or water gloves. If you have none of them, your melee attacks are Neutral. Spell attacks have the element of the spell - fire bolt does Fire damage, and so on.
Damage you deal is determined by the elemental table (look in the manual under "help") - look up the correct attack and defence column, and multiply the modifier (which is in per cent) by the element level. For example, if you have Water (your attack) on Fire 2 (the opponent's defence), you deal 25 x 2 = 50% additional damage. If you use Water on Water 4, you deal -25 x 4 = -100% damage - so your spell would be completely blocked. If you used Water on a Water 5 monster, it would actually drain the spell (you deal -25 x 5 = -125% damage) and recover health.
So, if you use a water enchantment potion, and wear a water glove, your defence element will be Water 1 (Water 2 if you have the water gem), and your melee attacks will be Water as well. if you use a water enchantment potion, and wear a fire glove, your defence element will be Water 1 (Water 2 if you have the water gem), but your melee attacks will be Fire.
