Are there any denominations that believe in "Eternal Security" but deny "Perseverance of the Saints" or vice versa?

Difference in origin and groups

Perseverance of the Saints (POTS) is the "P" of the TULIP formulation of early Calvinism, conceptually originating roughly from the 5 article headings of the 1618 Canons of Dort, although the acronym came later. It is founded on the Calvinist doctrine of unconditional election (the "U").

Eternal Security or Once Saved Always Saved (OSAS) came later (although conceptually it was earlier), held by Baptist groups who don't subscribe to unconditional election, but base the eternal security on Jesus' promise. Their theology is not full Calvinism but goes back to St. Augustine, now sometimes labeled Free grace theology. This probably happened due to the influence of Wesleyan revival compromising the doctrine of Predestination.

So what's the difference if the result is the same? One forum poster smartly said that:

"Eternal security" is simply a Free Grace [theology] relabeling of "Perseverance of the Saints"

Difference in the "experiencing"

But as blog article Five Differences Between Perseverance of the Saints and Eternal Security shows (emphasis mine):

[First two points I used in the previous section above]

Third, POTS and OSAS have different views of the condition of salvation. This comes out clearly when POTS advocates say that people who fall away into error or unbelief never truly believed to begin with. In effect, POTS advocates typically teach that you are born again or justified by a continuous faith that must be the “gift” faith that God only gives to the elect. Essentially, salvation does not only depend on what you believe, but how you believe it. By contrast, OSAS says there is only one kind of faith (persuasion that something is true) and that what matters is what you believe, not how you believe. Salvation requires a single act of faith in Jesus for eternal life (John 3:16, 36; 5:24; 6:47).

Fourth, POTS and OSAS take different perspectives on sanctification. According to POTS, sanctification is unconditional. Since the elect are predestined to salvation, and God causes them to be sanctified, they will never fall into major sin or unbelief in this life but will persevere in faith and good works until death. By contrast, OSAS sees sanctification as conditional. You have to choose to be a doer of the word to be sanctified, and there is no guarantee that you will progress from a carnal state to a spiritual one. But believers are eternally secure whether they experience practical sanctification or not.

Fifth, POTS and OSAS have different effects on assurance. Under POTS, you cannot be sure of your salvation because you cannot be sure if you are one of the elect with special gift faith who will persevere in faith and good works until death. By contrast, for OSAS, assurance is not only possible, it is the essence of saving faith. Jesus promised believers everlasting life (John 3:16; 5:24; 6:47; 11:25-26). Hence, you cannot believe that promise without believing the life He gives is everlasting.

Ken Hamrick's post explains in a lot more depth the differences summarized above.

Conclusion

The two labels survive because they help distinguish the two kind of salvation "experience" and in so doing clarify discussions and reduce confusion as the two concepts have quite different content after investigation.

Although the result is the same, because the doctrine's content is different, the experience of the salvation journey is also different. In addition:

• Baptist groups who label the experience as "Eternal Security" usually don't subscribe to the full TULIP, so they deny "Perseverance of the Saints"
• Calvinist groups who label their doctrine as "Perseverance of the Saints" in full fidelity to their theological tradition will deny "Eternal Security" doctrine once they realize it doesn't necessarily have the critical component "Unconditional Election"