I was looking thru some ship weapons at the exchange and I was wondering if battle crusiers and cruisers are the same in regards to weapons. I don't see cruisers listed at all, only battle cruisers.

No, you are talking about Cannons I guess. Only Federation escorts can mount those, for the Feds. Klingons can mount them on their Battle Cruisers as well.

It would help if you defined what you meant, as there is no "battle cruiser" in the game.

Ship weapons are not specific to ship class - your character has to be of a certain rank to equip a givem mark of weapons.

Lt. gets Mark I and II gear equippable.
Lt. Cmdr gets Mark III and Mark IV.
Commander gets Mark V and Mark VI.

And so on, until you get to Admiral and Mark X-XI gear.

An Admirla flying a Miranda could use Mark XI weapons on it... if the player wanted to.

Ok, makes sense...thanks!

The Sovereign, Noble, and Majestic classes are considered 'battle cruisers' in STO.

FYI there is limits to weapon types on certain classes of ships.

You can not put a cannon on a cruiser or science ship, though I did see someone with the heavy version of the cannons (the ones with the big ball at the end of the energy bolt thing) firing those off of a science ship but if your talking traditional cannons like on the deffiant those are assault only and it says so in the tool tip.

Actually, they're Assault Cruisers.

Battle Cruisers are klingon cruisers.

That is an ability not a Cannon. It's some Science BO reflective damage ability, Feedback something, which causes your shields to reflect energy damage back to the attacker.