I have one road bike with 6 speeds freewheel. I have 7 speeds freewheel is fit between the dropouts. But the last the 14 tooth i try that is touch on the dropout. I see the axle have the wheel now is short for 7 speeds. How i repalce the axle with longer. I see difference between 6 and 7 speeds or not. Because the freewheel 6 speeds is working okay on the bike i should ride the bike like that and i not worry why i not have one more gear? And i have wheels fulcrum racing 7 with 9 speeds cassete. That wheels is fit in the old steel bike with the 6 speeds freewheel. Only i do when i put the wheel i have open the dropouts with my hands some hard for fit the wheel. The bike is ride okay like that. i want find good light weight wheels. All wheels 8-9-10 speeds freehub is have same size different brands wheels?

Lots of issues in one post.

First- 7 speed freewheels (or cassettes, there's a difference that you need to be sure of) are a bit wider then 6 speed ones. It only takes a few mm's more cog width to have the chain contact the frame/dropout. While a axle spacer could be added to get the RH end of the axle to stick out further then the 7 speed FW does it's not like more gears will make you a better rider. So the easiest is to stick with what works already, the 6 speed cog set.

The fancy wheels likely have a longer axle, the 6 speed might be a 126mm long axle lock nut out side to locknut out side, the fancy ones are likely a 130mm axle width. So some frame spreading is needed to install the fancy wheels.

All of this wheel and cog count refitting is over laid on the possibility of the bike having an indexed gear system. this means that without a friction shifter option the cog count needs to remain the same as the shifter or problems will occur.

I suggest that the Op does some more homework before changing anything. Andy.

Dropouts must bear squarely on hub for good axle life.

I think you should respace the frame properly or leave it as a 6-speed.

7 speed freewheel axles will not last as long even if properly respaced.

your standard spaced 6 speed freewheel and the narrowly spaced 7 speed should both fit in a 126 wide frame
they were made to be so.

It is so on mine. yes the dropouts need be square to the axle.. run by a bike shop to have that checked .