What’s the difference between a validation by nodes and a verification by miners?
The rules by which a full node verifies a transaction are defined here in the Wiki, and here. 

Full node or mining node both validate against the same set of rules. If they don't follow the rules, they have to carry the consequences and might get blocked/banned, if forwarding wrong information to the network. 

Independent from Bitcoin, there is a difference between the two words, be it in software development or project management. verification is like a check list, were each parameter is checked against some specs ("the system complies with specification"). And validation is more process oriented ("the system meets the intended needs for a user"). 

In the  case of full nodes/mining node, both follow the verification in the same way, just after verifying against the specs, the miner follows  additional steps, and is eventually lucky to get the tx in the block and find the reward.