Yup, for six or seven or eight cog freewheels or freehubs, go with an eight speed chain, Schram being my personal choice, thanks to easy breaking for maintenance purposes.

And, yes, nine, ten or eleven speed chains will not fit your "clusters". To that, add this...

If you chain is worn, how about your crank rings and the freewheel cogs? They too could be worn, making a new chain a poor fit. Perhaps you would be wise to send us some good clear detailed pictures of your cogs and rings. Armed with those, more precise help might be available here.