Is it normal to be able to lift a higher weight amount on one machine at the gym and not be able to lift the same amount on another machine that is working the same muscle.. for example the chest. I noticed that when I am using a compound machine that targets Chest and tris I can lift 70lbs (3 sets of 10) but when I am using the pec fly machine, I struggle my sets at 60lbs... is this normal? Am I doing something wrong? Keep in mind I have been only doing this 3 weeks now.

I absolutely believe you will see you'll need different weights for different machines that target similar muscle groups, even with machines that do the same movement, depending on its range of motion, hand positioning, etc. that's my experience, at least, especially when you are targeting building power and muscle mass by using a high percentage of your single rep max weight.

Some machines make you work more through the range of motion, some machines let you "cheat", even if you aren't trying to, by giving you control that you wouldn't have with free weights.

Right now you should be focusing on good form and getting used to the machines, learning how to engage the muscles...

What is your goal? General fitness? Endurance? Size? Power?

Absolutely. You can bench a much heavier weight than you can fly. You'll also found that you can shift heavier weights on machines than free weights, but you'll get better results with free weights.

I am a certified personal trainer but I make my living as an equipment repair tech. I get the same question often from the club members . When doing isolation exercises on the machines often your body is locked to avoid assistances from any other body parts. They are great to isolate a muscle . It is not really meant for increasing strength. Problem with machines is that they only have a few adjustment setting and you will find some machines more user friendly or comfortable than others. Thus you are able to move a little more weight than on other machines. Angles and grips are also a issue. To increase strength you need to include freeweights . You will be able to move more weight being that all your stabilizer muscle will be involved to assist on your lift. Also your movement is more natural. So you will see a difference from exercise to exercise.