well for me its Battleship (federation real never had any of these
		
		
	 
Agreed.
	
		
	
	
		
		
			battle cruiser (again feds don't really use this but Akira may count as one)
		
		
	 
Possibly, mostly based on BTS data, the Prometheus-class - despite relatively modest size is probably a better example in 
firepower terms (to the extent that battlecruiser (mostly a European thing) is different from an American heavy cruiser (hull-coded as an "attack cruiser"). 
	
		
	
	
		
		
			heavy cruiser (most powerful in starfleet)
		
		
	 
True. 
Largely 
equivalent to a battlecruiser, but more balanced towards non-defense applications, probably greater range and endurance.
	
		
	
	
		
		
			cruiser - 1/2 of a heavy cruiser
		
		
	 
	
		
	
	
		
		
			light cruiser of 1/2 a cruiser
		
		
	 
Honestly, in space terms is mostly likely to be 
technical advancement than anything else that disambiguates these (the previous (battle)cruiser design is "demoted" to CL when the new one comes online). However, the closest comparable we have in canon (the Connie (heavy) cruiser [equivalent to a Klingon battlecruiser] and the Miranda light cruiser are broadly equivalent offensively speaking (the 
Reliant-subtype may actually be 
more heavily armed, unlike say the 
Soyuz (recon?), 
Lantree (reserve logistics) and Saratoga II (generalist)) so it might be a "speed and/or endurance thing" due to significantly reduced fuel tankerage space on the 
Miranda.   
	
		
	
	
		
		
			frigate- 1/2 of a cruiser.
		
		
	 
Pretty much. Definately something of a "moving target" label - the Connie was a (heavy)cruiser for 
it's era, but the broadly size equivalent 
New Orleans and 
Intrepid-classes are more likely to be the frigates of 
theirs. 
Frigates may also be somewhat more weighted towards a particular specialism than the big ships. 
	
		
	
	
		
		
			destroyer - starfeet really doesn't use this but the defiant would count.
Scout (1/4 of a frigate)
		
		
	 
Complicated due to multiple contradictory meanings of "destroyer". 
Guided Missile Destroyer - basically a cruiser with somewhat depreciated "flagship" capacity. 
Destroyer Escort - Classified as Frigates by the RN (and the USN post-70s)
Escort Destroyer - Dedicated ASW platform [no real parallel in space terms]. 
Torpedo Boat Destroyer - fast, long range escort vessels, mostly use torpedoes for offense, defensive guns. Defiant is largely
 trying to be this.
Torpedo Boat - relatively slow, short-to-medium range, carries both torpedoes and dual purpose guns (up to 5"). Defiant mostly sits here (crossed with the monitor). The Raider-type is either this or TBD.
	
		
	
	
Yup. 
	
		
	
	
		
		
			starship is interchangeable with any of these
		
		
	 
Mostly with frigates and above IMO, but "technology marches on" will effect this.