They mean the same thing, the same reality.
In Numbers both words are used interchangeably in Numbers 14:23 ("not one of them will ever see the land I promised in oath") and Numbers 14:30 ("not one of you will enter the land I swore with uplifted hand").
They are, thus, identical semantically in two ways:
- Linguistically, for "see" is used to signify not only physical beholding, but:
it is usual to use word "see" as "to get there", "enter there", or "come to there", as in expression, "long suffering Odysseus wanted to see his native Ithaca", or in 1 Peter 3:10 "whoever wants to see good days, let him abstain from evil tongue". In the first case Odysseus wants not to look at his native island, but to return there for good; and in the second case, Peter does not promise his reader just seeing good days as a neutral observer, but to live a good life.
- Expressing the same spiritual reality.
"Entering the Kingdom" and "Seeing the Kingdom" is one and the same thing, for this Kingdom is invisible and eternal, for as Paul says "We fix our eyes not on what is seen, but on what is unseen, for visible is temporal, but invisible - eternal" (2 Cor.4:18); now, how can one behold, or "fix eyes" on invisible? This oxymoron simply means that we also possess intellectual eyes that behold the invisible divine realities, that are imperishable. Exactly gathering those realities - love, wisdom, courage, mercifulness, in short, the gifts of the Spirit (cf. Gal. 5:20-23) is to establish the Kingdom of Heaven in us, through gathering and cultivating those treasures in our hearts, for "where is your treasure, there will be your heart" (Matt 6:21). However, how can we gather that which we do not see with eyes of our minds? Thus, seeing must precede and always accompany the gathering and cultivating of the gifts of the Spirit, which we can after having been born in the Spirit (John 3:3).
Thus, that in us that absorbs the spiritual gifts, the "inner man" (2 Cor. 4:16), or soul that unites the Lord, becomes one with the Spirit of Lord (1 Cor.6:17), and this Spirit will teach us, that is to say, give us vision of the eternal realities, for without Spirit it is not possible to see them. That is why Jesus says to His disciples that the Spirit will teach them the things they do not understand by their own unaided intellects (John 16:13).
Now, in the case of a physical vision, it is possible to see something from afar and not be there, for instance, if you see a beautiful lake but have to cross fields and mountains to get there, but in the case of the intellectual vision of invisible divine realities through the aid and enlightenment of the Spirit of God it is impossible to see and not have it, for there is nothing between the viewer and those eternal gifts revealed by the Spirit, for what you see in the light of the Spirit, that you also absorb and possess; to make perhaps a clarifying analogy: if one sees a funny point in a joke, he immediately laughs, for there is nothing between the vision of the funny point and the laughter (even if you intentionally suppress laughter for any reason, it still proves that the laughter has been there, for it should be/exist priorly in order to be suppressed); similarly, for instance, when you understand/view the divinity of Christ through the Spirit you also worship Him in praise, immediately calling Him "Lord Jesus"(1 Cor. 12:3), and when you worship God in Spirit, then you already are in His Kingdom, for what is the "entering of the Kingdom of Heaven" if not worshiping God in Spirit and Truth? (John 4:23).
Therefore, "seeing" and "entering" in this context denote the same spiritual reality.