Yes, the laws written in stone are the same as those written in our hearts, God did not change or alter them.
The difference was explained by Christ's sermon on the mount (Matthew 5). The Pharisees knew the law, but misconstrued it for their own benefit. They might beat a person within an inch of their life, but not kill them, thereby technically keeping the law "thou shalt not murder". That to me is what Jesus meant when he said that you can commit adultery in your heart without actually committing the sin physically. Keeping the letter of the law did not necessarily make a persons heart right, because it often omitted the purpose of the law, which was to "love thy neighbor as thyself" jmo
The difference was explained by Christ's sermon on the mount (Matthew 5). The Pharisees knew the law, but misconstrued it for their own benefit. They might beat a person within an inch of their life, but not kill them, thereby technically keeping the law "thou shalt not murder". That to me is what Jesus meant when he said that you can commit adultery in your heart without actually committing the sin physically. Keeping the letter of the law did not necessarily make a persons heart right, because it often omitted the purpose of the law, which was to "love thy neighbor as thyself" jmo