Does 85% lean ground turkey have the same amount of fat as 85% lean ground beef?
Yes.

"85% lean" means that 15% is fat... regardless of the type of meat.

"95% lean" means that 5% is fat... 

Much of ground turkey is made from turkey breast, which is naturally nearly fat free, which is why it's often sold as "99% fat free", meaning there's only 1% fat.

The turkey that's 85% lean is usually dark meat - legs and thighs - which are significantly higher in fat than the breast meat. This is generally standard for most (if not all) fowl. 

Here's some numbers: 


  Ounce for ounce, white turkey breast meat trumps dark meat, calorically speaking. Per 3 ounces, opting for white meat over dark will save you 45 calories and 6 grams of saturated fat: 115 calories and 0 grams of saturated fat versus 160 calories and 2 grams of saturated fat, respectively. 


In general, sources tend to say that dark meat is more flavorful and more moist, which is generally true of higher-fat proteins.

Beef doesn't have as many sections that are similarly lacking in fat and ground beef is often made from trimmings from all sorts of parts of the cow, not just one part.

As a note, I regularly see ground beef as low as 70% lean (this is the lowest it can be - as stated by USDA law)... but I've never seen turkey lower than 85%, that I can think of.