The after tax contributions are held in a separate sub account with earnings on those contributions. The “non taxable” balance could be the after tax contributions, while the higher after tax balance may include both the contributions and their earnings. Normally, you would request a split direct rollover per Notice 2014-54 in which you order in a single request that the after tax contributions (not their earnings) be directly rolled to a Roth IRA and the entire pre tax balance of the account to your rollover TIRA. There would be no taxes due for these rollovers.
In addition, you should consider the feasibility of NUA on the employer shares if the cost basis of those shares is under 25% of their current value. This will increase the complexity of your distribution, since with NUA the shares that you choose will be transferred to your taxable brokerage account and whenever you sell them you only owe the lower LT cap gain on the NUA amount. If you do not want to use NUA for all these shares, you can choose the ones with the lowest cost basis and roll over the rest to your TIRA. Again, the decision planning is complex, so you would probably need professional help with it if you want to utilize NUA for part of your distribution. You would start with a quote from your plan on the cost basis of these shares, separately if there are spin off company shares in the plan. If the cost basis is too high, then you forget NUA and go by the first paragraph above only.