About This Answer
Is samādhi the same as jhāna? Ajahn Dtun asks the questioner not to get caught in scriptural terminology. What matters is developing peace of mind as much as possible and knowing whether it is a little or a lot peaceful; for exact definitions, look in the books.
In his 44 years as a monk, he says, he has never thought about what level of samādhi he was in, and no sign ever appeared announcing first, second, third or fourth jhāna. All that is needed is a mind peaceful enough to have the energy and strength to let go of attachment and identification with mental states and the body. Studying definitions brings little benefit compared with seeing within one's own heart.
He agrees with the questioner's description: at coarser levels there is joy or rapture, then deeper happiness, and as concentration deepens the mind becomes one-pointed and equanimous.