The terms Second home and Rental home are not at all interchangeable and may be differentiated according to overall purpose or intention. 

Basically, a second home is the same as a vacation home, or is a place that is occupied on occasion. Since they aren't rented out/used only by the owner, then there really isn't an increase in the rates for this property (vs. the first home).  You can expect to find a charge for  1/4 point increase in discount point.  Depending on the lender, the rates for a first and second home are exactly the same.

The rental home is used to generate additional income by collecting rent.  The only problem is that some lenders will charge a higher rate for a loan on this type of property.  In addition, these types of homes will also require for the owner to put down a higher payment with this higher interest rate.  It all comes down to risk, and the fact that the risk involved with this type of transaction (investment) is higher.  These rates, then, will most likely increase by 25-37.5% in rate (150 basis points), with investment loan minimum down payments beginning at 10%.  On top of this, expect an increase in the mortgage insurance premium on investment loans.  You won't find any competitive rental rates unless you can afford to put down 20%.  

Basically, the way that the two of these are determined (by the lender) are: 1) type of property and 2) appraisal and rent survey.  Honestly, it's not good to try to disguise the fact that the rental property is a second home (for financial savings) because it hardly works.  

Bankapedia's Take

Let's say that you have a lot of money or just like to collect inexpensive homes. You already have a primary residence a second home in Nantucket. You recently got a big bonus and want to buy another vacation home, somewhere warm, maybe Tucson. While you don't plan on renting the property, the bank will not care, and this property will receive the same financing terms as if it was an investment/rental property. It comes down to which home are you going to let go of if things go upside down for you. Not your primary, that's for sure. 

Something else to note. if you are planning to buy an investment/rental home but want to cheat the system and claim its a vacation property to get a lower rate, the property will need to be quite a large distance away from your primary. This means: at least 50 miles. And, it will also need to be in an area that one would consider a vacation area--definitely not a slum in Detroit.  

So now you know, and knowing is half the battle.