One way to differentiate between the public use of tongues and the private use of tongues is to classify the private use as praying in tongues and the public use as speaking in other tongues. Paul mentions both uses in the fourteenth chapter of his first letter to the Corinthians. What are the differences?
When we pray in tongues, our spirits are praying to God (see 1 Cor. 14:2, 14). Yet, when someone is suddenly anointed with the gift of various kinds of tongues, it is a message from God to the congregation (see 1 Cor. 14:5), and it is understood once the interpretation is given.
According to Scripture, we can pray in tongues as we will (see 1 Cor. 14:15), but the gift of various kinds of tongues only operates as the Holy Spirit wills (see 1 Cor. 12:11).
The gift of various kinds of tongues would normally be accompanied by the gift of the interpretation of tongues. The private use of praying in tongues, however, would normally not be interpreted. Paul said that when he prayed in tongues his mind was unfruitful (see 1 Cor. 14:14).
When an individual prays in tongues only he is edified (see 1 Cor. 14:4), but the entire congregation is edified when the gift of various kinds of tongues is in manifestation with the accompanying gift of the interpretation of tongues (see 1 Cor. 14:4b-5).
Every believer should pray in tongues every day as part of his daily fellowship with the Lord. One of the wonderful things about praying in tongues is that it doesn't require the use of your mind. That means you can pray in tongues even when your mind must be occupied with your work or other things. Paul said to the Corinthians, "I thank God, I speak in tongues more than you all " (1 Cor. 14:18, emphasis added). He must have spent a lot of time speaking in tongues to outdo the entire Corinthian Church!
Paul also wrote that when we pray in tongues, we are sometimes "blessing the Lord" (1 Cor. 14:16-17).