Training tires are plenty fast enough to train on and they can be used for racing. They will generally be a bit less grippy than a full on racing tire, probably a bit stiffer riding and will yield more miles (and often more maintenance-free miles than the equivalent racing model in the same brand.
Training tires may have a harder, longer wearing rubber compound, thicker tread area and maybe a heavier sidewall. Sometimes the manufacture will add some space age named anti-puncture belt to the mix. It all adds up just a little less race characteristics and a bit more weight.
A cement block? Not unless you buy a real clunker tire model.
Go to the various websites. Compare a Michelin Pro 4 Race to a Pro 4 Endurance to the Pro 4 Service Course. The difference in grams from flyweight pro-issue to a near touring durable tire...all in the same line up...isn't much.
There will be differences and yeah, experienced riders can 'feel' them and do select their tires accordingly. But, you're not going to go from 'I rule the group rides!' to Spit out the back!' due to switching from a light race day tire to a decent training tire.
My recommendation is to try a pair of Vredestein Fortezza Tricomps. They are plenty light, take ridiculous pressure, have a great carcass for ride quality, offer decent grip in the dry and puncture less than any tire I've ridden. Some of the fast cats up here are on Kendas and they seem to like their training rubber.