After some conversations with knowledgeable folks, it seems there are indeed some differences between Arminian and Catholic soteriologies. Here’s how I’d formulate Catholic teaching (with thanks to Jimmy Akin and Wikipedia). I cannot guarantee it is free of error.
Total Deparavity: God gave man free will so that we might choose freely to love Him. Unfortunately, the Fall impaired our free will. Grace restores our unfallen goodness, if only for a time (i.e until we sin).
Semi-Conditional Election: God has told us through Scripture that there is a guaranteed way to be saved. We must accept Jesus Christ by our own free will and live by His commandments. However, God also saves whomever He wills, and we, as mere mortals, have no right to judge which individuals will and will not receive eternal life. We may only say that certain actions are contrary to God’s law and unpleasing to Him.
Unlimited Atonement With Limited Intent: Jesus Christ died for all mankind, but the saving grace He made available is only guaranteed to be efficacious if we accept Jesus Christ by our own free will and live by His commandments. By opening ourselves to grace through faith, we become members of the elect who shall receive eternal life.
Irresistable Grace: The sacraments of initiation, baptism and confirmation, confer grace unconditionally. That is, one need not already be in a state of grace to receive the grace conferred by these sacraments.
Resistable Grace: Grace is not forced upon us. We open ourselves to grace and by doing so restore the free will we were intended to inherit from our progenitors. Grace is conferred conditionally in the Eucharist and annointing of the sick. We must already be in a state of grace to participate in those sacraments. For instance, if we take the Eucharist unworthily, we eat and drink condemnation upon ourselves.
Uncertain Perceverance: Membership in the elect is not made permanent at initiation. God gives us sustaining grace, spiritual sustenance if you will, if we ask for it and through sacraments. However, there are choices we can make (i.e sins we can commit) that separate us from God and remove us from the company of the elect. Like Paul, we must work out our salvation with fear and trembling and strive to finish the good race. We must also seek sustaining grace through praying, reading scripture, receiving the sacraments, etc. In particular, the sacrament of confession restores us to a state of grace if are truly contrite and repentant. There is no such thing as "once saved, always saved" according to the Church. We were saved by Christ’s salvific act. We are being saved as we grow in faith. We hope to persevere to the end and be saved at the judgement.
Questions? Comments? I’m not sure where to put marriage and holy orders. Any suggestions?