According to Catholicism, is the blessing of food by a lay person different from that of a priest? I am a bit puzzled. On the one hand, it is common practice among families to ask God to bless the food to be eaten. According to this very related question, the Catechism states:


  every baptized person is called to be a "blessing," and to bless. Hence lay people may preside at certain blessings; the more a blessing concerns ecclesial and sacramental life, the more is its administration reserved to the ordained ministry (bishops, priests, or deacons). 


Yet, according to the Catholic Encyclopedia:


  [in a] strictly liturgical and restricted sense, blessing may be described as a rite, consisting of a ceremony and prayers performed in the name and with the authority of the Church by a duly qualified minister, by which persons or things are sanctified as dedicated to Divine service, or by which certain marks of Divine favour are invoked upon them.


The same article states that from very early times, the Church has considered blessing an ecclesiastical institution.

Later on, it says:


  Priests, then, are the ordinary ministers of blessings, and this is only in the fitness of things since they are ordained, as the words of the Pontifical run: "ut quæcumque benedixerint benedicantur, et quacumque consecraverint consecrentur" (That whatever they bless may be blessed, and whatever they consecrate shall be consecrated). When, therefore, laymen and women are represented as blessing others it is to be understood that this is an act of will on their part, a wish or desire for another's spiritual or temporal prosperity, an appeal to God which has nothing to recommend it but the merits of personal sanctity. The ordinary greetings and salutations that take places between Christians and Catholics, leavened by mutual wishes for a share of heavenly grace, must not be confounded with liturgical blessings.


Does this mean that the blessing of food given by a priests (say, if you invite one to your house) is of a different nature that the blessing of food given by a lay person?

In my view, the different sources are, if not contradictory, rather imprecise, in particular when it comes to the comparison of the nature of both priestly and lay blessing.

Naturally, my question refers to blessings of things in which lay persons are traditionally involved (like food or family members), but not things which are traditionally reserved to priests (like holy water).
If I understood your question correctly, you are asking what the difference between a priests and a normal persons blessings are, right? Well, you almost found the right spot in the Encyclopedia, since, in the very same article we find:

The inquiry will be confined to the Blessings approved of by the Church. As has been said, the value of a blessing given by a private person in his own name will be commensurate with his acceptableness before God by reason of his individual merits and sanctity. A blessing, on the other hand, imparted with the sanction of the Church has all the weight of authority that reaches to the voice of her who is the well-beloved spouse of Christ, pleading on behalf of her children. The whole efficacy, therefore, of these benedictions, in so far as they are liturgical and ecclesiastical, is derived from the prayers and invocations of the Church made in her name by her ministers. (emphasis mine)

So, a blessing from a priest does have a special meaning, although your food usually is not thanked for in mass or some other sacramental rite(this is possible at home, but I do not think a priest would call thanking for food sacramental).
Should this - for whatever circumstance - be the case, however, the Encyclopedia has the following benefits that may come from such a blessing and states that they are more likely to happen due to the authority of the church which is far larger then that of men:

1.Excitation of pious emotions and affections of the heart and, by means of these, remission of venial sin and of the temporal punishment due to it;
2.freedom from power of evil spirits;
3.preservation and restoration of bodily health.
4.various other benefits, temporal or spiritual.