Is a baptized but not confirmed Catholic really a Catholic?

Short answer: Yes, that is incorrect, because baptism in the Catholic Church makes you Catholic

CCC 1213

Holy Baptism is the basis of the whole Christian life, the gateway to life in the Spirit (vitae spiritualis ianua), and the door which gives access to the other sacraments. Through Baptism we are freed from sin and reborn as sons of God; we become members of Christ, are incorporated into the Church and made sharers in her mission: "Baptism is the sacrament of regeneration through water in the word."

From CCC 1227

The baptized have "put on Christ." Through the Holy Spirit, Baptism is a bath that purifies, justifies, and sanctifies.

From the Nicene Creed: I confess one baptism for the forgiveness of sins.

The ideal path to receiving sacraments of initiation

1. The Easy answer is for children/minors: you are a Catholic when baptized

   Baptism received by a child or infant receives is the full sacrament of Baptism. (It's not a kid's meal, it's the full serving). During further faith formation the child is catechized and typically receives the sacraments of penance and reconciliation, and then receives the Eucharist around the age of reason (about 7 years old). While the eventual goal is to continue catechizing and confirm the child they approach adulthood, the minor is not a partially Catholic. Baptism has taken care of that. (CCC 1227)

2. For Adult Entering the Faith (ideal case)

   The restoration of the Catechumenate and the institution of the Rite of Christian Initiation of Adults combines the reception of all three sacraments into one rite (Baptism, Eucharist, and Confirmation) sacraments of initiation, CCC 1212-1419 typically at the Easter Vigil mass. (Canon Law allows for other methods of reception at the discretion of the local ordinary/bishop).

   Can. 881 It is desirable to celebrate the sacrament of confirmation in a church and during Mass; for a just and reasonable cause, however, it can be celebrated outside Mass and in any worthy place.

   When this ideal path to entering into the Catholic communion is followed, the question never arises.

What about the less than ideal path, which is where your question is coming from?

First off, let's take a look at confirmation. What is confirmation?

Can. 879 The sacrament of confirmation strengthens the baptized and obliges them more firmly to be witnesses of Christ by word and deed and to spread and defend the faith. It imprints a character, enriches by the gift of the Holy Spirit the baptized continuing on the path of Christian initiation, and binds them more perfectly to the Church.

Even from the canon law perspective, the person is recognized as being in the Church (being Catholic) through Baptism; Confirmation "binds them more perfectly."

The Church does not penalize any of the faithful who were baptized as children, but who for one reason or another were not confirmed. (CCC 1227 as above: one baptism). What the church, both laity and clergy, are called to do is to encourage those baptized, but not yet confirmed, to undertake further faith formation and catechisis and then receive the sacrament of confirmation. (CCC 1306-1311)

1306 Every baptized person not yet confirmed can and should receive the sacrament of Confirmation. Since Baptism, Confirmation, and Eucharist form a unity, it follows that "the faithful are obliged to receive this sacrament at the appropriate time," for without Confirmation and Eucharist, Baptism is certainly valid and efficacious, but Christian initiation remains incomplete.

Bottom Line: even when Confirmation is delayed, the baptized Catholic is still Catholic.

More on the "ideal" case

Christian Initiation

1229 From the time of the apostles, becoming a Christian has been accomplished by a journey and initiation in several stages. This journey can be covered rapidly or slowly, but certain essential elements will always have to be present: proclamation of the Word, acceptance of the Gospel entailing conversion, profession of faith, Baptism itself, the outpouring of the Holy Spirit, and admission to Eucharistic communion.

1230 This initiation has varied greatly through the centuries according to circumstances. In the first centuries of the Church, Christian initiation saw considerable development. A long period of catechumenate included a series of preparatory rites, which were liturgical landmarks along the path of catechumenal preparation and culminated in the celebration of the sacraments of Christian initiation.

1231 Where infant Baptism has become the form in which this sacrament is usually celebrated, it has become a single act encapsulating the preparatory stages of Christian initiation in a very abridged way. By its very nature infant Baptism requires a post-baptismal catechumenate. Not only is there a need for instruction after Baptism, but also for the necessary flowering of baptismal grace in personal growth. The catechism has its proper place here.

1232 The second Vatican Council restored for the Latin Church "the catechumenate for adults, comprising several distinct steps." The rites for these stages are to be found in the Rite of Christian Initiation of Adults (RCIA). The Council also gives permission that: "In mission countries, in addition to what is furnished by the Christian tradition, those elements of initiation rites may be admitted which are already in use among some peoples insofar as they can be adapted to the Christian ritual."

1233 Today in all the rites, Latin and Eastern, the Christian initiation of adults begins with their entry into the catechumenate and reaches its culmination in a single celebration of the three sacraments of initiation: Baptism, Confirmation, and the Eucharist. In the Eastern rites the Christian initiation of infants also begins with Baptism followed immediately by Confirmation and the Eucharist, while in the Roman rite it is followed by years of catechesis before being completed later by Confirmation and the Eucharist, the summit of their Christian initiation.